excel
Chapter 8: Trendlines and Regression Analysis
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Linear y = a + bx
Polynomial (2nd order) y = a +bx + cx2
Polynomial (3rd order) y = a + bx +cx2 + dx3
Logarithmic y = a +bln(x)
Power (log-log) y = axb or Exponential y = abx or
Note: The base of natural logarithms is e = 2.71828…
Common Mathematical Functions Used in Predictive Analytical Models:
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Modeling Relationships and Trends in Data
Create charts to better understand data sets.
For cross-sectional data, use a scatter chart.
For time series data, use a line chart.
Right click on data series and choose Add trendline from pop-up menu
Check the boxes Display Equation on chart and Display R-squared value on chart
Excel Trendline Tool
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R2 (coefficient of determination) is a measure of the “fit” of the line to the data. The value of R2 will be between 0 and 1. A value of 1.0 indicates a perfect fit and all data points would lie on the line; the larger the value of R2 the better the fit.
Example 8.1: Modeling a Price-Demand Function
Scatter chart with the linear demand function
Sales = 20,512 - 9.5116(Price)
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Predicted Sales decreases by 9.5116 per $1 increase
in Price.
Regression analysis is a tool for building mathematical and statistical models that characterize relationships between a dependent (ratio) variable and k independent, or explanatory variables (ratio or categorical), all of which are numerical.
Simple linear regression involves a single independent variable; the k = 1 case.
Multiple regression involves two or more independent variables; the k > 1 case
Regression Analysis
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Finds a linear relationship between:
- one dependent variable Y and
- one independent variable X
First prepare a scatter plot to verify the data has a linear trend.
Use alternative approaches if the data is not linear.
Simple Linear Regression
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Example 8.3: Home Market Value Data
Size of a house is typically related to its market value.
X = Square Footage
Y = Market Value ($)
The scatter plot of the full data set (42 homes) indicates a linear trend.
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Predicted Market Value = + (Square Feet)
Two possible lines are shown below.
Line A is clearly a better fit to the data.
We want to determine the best regression line.
Finding the Best-Fitting Regression Line
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Predicted Market Value = 32,673 + 35.036(Square Feet)
The estimated market value of a home with 2,200 square feet would be: $32,673 + $35.036(2,200) = $109,752
Example 8.4: Using Excel to Find the Best Regression Line
The regression model explains variation in market value due to size of the home.
It provides better estimates of market value than simply using its average.
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Simple linear regression model:
We estimate the parameters and from the sample data to find the estimated regression line:
and are the point estimates of and
Let Xi be the value of the independent variable of the ith observation. Then is the estimated value of Y for Xi.
Least-Squares Regression
Note: The error term ε is assumed to be normally distributed with a zero mean and a constant unknown standard deviation σ.
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Residuals are the observed errors associated with estimating the value of the dependent variable using the regression line:
Residuals
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The best-fitting line minimizes the sum of squares of residuals (RSS = residual sum of squares):
Least Squares Regression
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Estimate Y when X = 1750 square feet:
= 32,673 + 35.036(1750) = 93,986, that is, $93,986
Data > Data Analysis >
Regression
Input Y Range (with header)
Input X Range (with header)
Check Labels
Excel outputs a table with many useful regression statistics. The regression
equation is shown by the column “Coefficients”
Simple Linear Regression With Excel
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Home Market Value Regression Results
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Predicted home market value increases by $35.04 per
1 square foot increase in Home Size
Multiple R: If k = 1, R = | r |, where r is the sample correlation coefficient. The value of r varies from -1 to +1 (r is negative if slope is negative)
R Square: coefficient of determination, R2, which
varies from 0 (no fit) to 1 (perfect fit). If k =1, R2 = r2
Adjusted R Square: adjusts R2 for sample size and number of X variables
Standard Error s: the estimated standard deviation of the error term ε; variability between observed and predicted Y values. This is formally called the standard error (of the estimate), s = SYX.
Regression Statistics
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Example 8.6: Interpreting Regression Statistics for Simple Linear Regression
53.47 % of the variation in home market values can be explained by home size.
The standard error s = $7287.7
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(X is not a significant variable)
(X is a significant variable)
Reject H0 means that the slope of X is not equal to zero. Using a linear relationship, X is a significant variable in explaining variation in Y.
Example 8.7: Testing Significance of the X Variable
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The t-test statistic for testing the significance of X
is is assumed to have the t distribution with df = n – k – 1 =
n – 1 – 1 = n – 2
Excel provides the p-value of the test.
(8.7)
Example 8.8: Hypothesis Test for the significance of Home Size (Square Feet)
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| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 32673.2 | 8831.95 | 3.6994 | 0.0006496 | 14823.18 | 50523.29 |
| Square Feet | 35.0364 | 5.1673 | 6.7803 | 3.798E-08 | 24.5927 | 45.4800 |
Since p-value = 3.798(10-8) reject to conclude that Square Feet is significant
The Lower 95% and Upper 95% values of the 95% confidence interval for can be also used to test:
Since the interval [24.5927, 45.4800] does not contain 0, should be rejected at a 5% significance level.
Residual = Actual Y value − Predicted Y value
Standard residual = residual / (standard deviation)
Rule of thumb: Standard residuals outside of ±3 show potential outliers.
Excel provides a table and a plot of residuals.
Residual Analysis and Regression Assumptions
This point has a standard residual of 4.53
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Linearity
examine scatter diagram (should appear linear)
examine residual plot (should appear random)
Normality of Errors
view a histogram of standard residuals
regression is robust to departures from normality
examine the normality plot in Excel’s Regression
Homoscedasticity (a constant variance of the error term ε): variation about the regression line is constant
examine the residual plot
Independence of Errors: successive observations should not be related.
This is important when one of the independent variable is time.
Checking Assumptions
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Examples of Diagnostic Scatter Charts of Residuals when the Regression Assumptions Are Not Met
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Linearity - linear trend in scatterplot
- no pattern in residual plot
Example 8.11: Checking Regression Assumptions for the Home Market Value Data
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Normality of Errors – residual histogram appears slightly skewed but is not a serious departure. Excel’s normal probability plot looks OK.
Example 8.11 Continued
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Constant Error Variance – residual plot shows no serious difference in the spread of the data for different X values.
Example 8.11 Continued
Independence of Errors – Because the data is cross-sectional, we can assume this assumption holds.
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- the linear model (Model 1)
Interpretation of : the change in when X increases by 1.
Poor results for the assumed model:
The Need for Variable Transformation; file UN11
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ppgdp Residual Plot
499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 2.8060619532387685 -1.5352000086793103 -0.89272548514221617 2.0954376205294913 -0.73775425831892294 -0.71262170489870202 -1.3458952580720365 -0.77540740167088429 0.59953364866214143 -0.38632366342129698 -0.84944522614334694 -0.58188857373310232 -0.16581653858598022 -0.99945132480312893 -1.1388354797477789 -1.5163837040073971 5.965326591540232E-2 -0.35499562947917829 1.9238118679765552 1.5471173855349225 -0.85437828634387891 0.11440333657504498 -1.9005750324397477 -0.32393583132048676 -1.0348922850509064 -0.14882235514948672 -1.4281570684740383 2.5887245853538952 0.87874153807370314 -0.73039230295781143 1.1477130877635835 -2.8429839240102783E-3 -0.79506726627703506 0.24826085251846997 1.2595190127581355 2.5823733143544665 -0.96537194195235387 -1.4795348195238625 -0.68571226412536834 1.5876678175167451 1.3494014423487206 -0.25618122026659584 -1.1193036572411807 1.0830324990657987 -1.2345326801165175 -1.5443068770954986 -0.81193598503945341 -1.0738 58797244267 2.3135098071926907 0.49428079809384085 0.45214593997371066 4.6832684080966303E-2 -0.5216005846606917 2.7626914755113652 -0.65454277494399138 -0.45696348548279841 -0.89725402994336312 2.3415541286742005 1.0788243694297179 -1.0234203378378446 0.68047919764079268 -0.46240948322709619 0.12164176832509033 7.500059749682797E-2 -0.35522702151422614 0.41622977409113115 1.5296260514233895 -1.5641119872092539 -0.44503751292696747 0.85276570736624269 -0.78949284736763081 0.16885050512692468 -0.76910033865358818 0.75435427787555742 1.8677731514884517 1.7163552062557308 -0.89200604717323939 7.0162818997188126E-4 -0.11705052182299269 -1.0221963937800616 -1.335479170150385 0.17742479345612971 -0.59489107182084533 -1.0285009708339357 -1.4235858291993628 1.3855303208156702 0.39865623948725459 0.66938823731124941 -0.617464568408022 -0.75908870828018804 -0.37891909072150143 -0.14661219575038098 -0.40347445331756315 1.4707549486233278 0.3690872211605476 0.5273705821085779 -0.52920913821135551 -0.6013766951497086 -1.3305760748700208 -1.1167291413624987 -9.5518245318886308E-2 1.8670860090319312 -0.40551909876710468 -1.3315725707165376 1.8693196231248199 -0.41466468752645325 1.3285938886940216 2.801529165436742 -0.33788815554940399 -1.3599551135311387 2.9582566723252248 -1.2665174706576792 1.3048098344105714 1.219296241160102 -1.3482020737054226 -0.65958719339477856 0.21482078924283465 -1.6758678116247678 -0.65999204929229505 -1.3395250459108095 -0.90319951611437954 1.5481329272226287 -1.2108634171078112 4.1136222559623903E-2 0.32024096920001099 -0.5737952464 4673729 -0.62740857578280096 0.11772476993017067 4.3708405643127612E-2 -6.6414444111977389E-3 -0.64167814986926475 3.7585387688007295 2.2927758600448498 -1.1737779906947758 1.4778752755272708 -0.36636650665729142 5.520200698016442E-2 -0.83149269419938676 1.1503327603897269 -0.52517826419472602 0.66681317487155978 -0.23120536904241806 -0.59470857043910819 -5.9404444629131525E-2 -1.3703517313615285 -1.179668056143236 -0.57386292729649191 1.343632976537565 -1.1150051777456438 -1.5091104913321947 -1.3175507689315422 2.1211279266413636 -1.0571695699272006 0.69211144720277584 0.35116834782301476 -3.1985269636250369E-2 1.4601463377722537 -1.4519117942603128 -0.47136404328191395 1.5613467015209825 -0.40936148954592722 -1.2945004986541606 -0.96113890527778145 0.90129374086947012 3.1087632450923106 -0.56267669200890547 -0.69619955688469126 -0.86687540726305379 -0.98534803712454577 1.1055056209414991 -0.68725694731624909 0.10208388725612982 0.31263515726594426 0.56302713154329975 -0.31207077043051834 1.0209507852061872E-2 2.3376061438647175 -1.6389579168539254 -1.5022503175241138 0.70288144029902178 0.7185072876183467 -1.0591779429803052 -1.1337570985569647 -0.83275524289806269 -0.71506020122038016 0.62411449680802811 2.7393820653716801 -1.5977576098548845 -0.20247691889582975 -0.14804669920870106 0.38907909053485179 -0.75230081645241675 -0.86822203746306048 0.66695358839479857 -0.35467383248715256 -1.3900519802340745 1.8060948735485218 3.1617118376182671 -5.0566015856357449E-2ppgdp
Residuals
fertility
fertility 499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 5.968 1.5249999999999999 2.1419999999999999 5.1349999999999998 2 2.1720000000000002 1.7350000000000001 1.671 1.9490000000000001 1.3460000000000001 2.1480000000000001 1.877 2.4300000000000002 2.157 1.575 1.4790000000000001 1.835 2.6789999999999998 5.0780000000000003 1.76 2.258 3.2290000000000001 1.1339999999999999 2.617 1.8 1.984 1.546 5.75 4.0510000000000002 2.4220000000000002 4.2869999999999999 1.6910000000000001 2.2789999999999999 1.6 4.423 5.7370000000000001 1.8320000000000001 1.5589999999999999 2.2930000000000001 4.742 4.4420000000000002 2.5308062840941101 1.8120000000000001 4.2240000000000002 1.5009999999999999 1.4510000000000001 1.458 1.5009999999999999 5.4850000000000003 1.885 3.589 3 2.4900000000000002 5.9180000000000001 2.3929999999999998 2.6360000000000001 2.1709999999999998 4.9800000000000004 4.2430000000000003 1.702 3.8479999999999999 2.6019999999999999 1.875 1.9870000000000001 2.0329999999999999 3.1949999999999998 4.6890000000000001 1.528 1.4570000000000001 3.988 1.54 2.2170000000000001 2.1709999999999998 3.84 5.032 4.8769999999999998 2.19 3.1589999999999998 2.996 1.137 1.43 2.0979999999999999 2.5379999999999998 2.0550000000000002 1.587 4.5350000000000001 2.097 2.9089999999999998 1.476 2.262 1.4179999999999999 2.8889999999999998 2.4809999999999999 4.6230000000000002 3.5 2.2509999999999999 2.621 2.5430000000000001 1.506 1.764 3.0510000000000002 5.0380000000000003 2.41 1.4950000000000001 1.6830000000000001 1.163 4.4930000000000003 5.968 2.5720000000000001 1.6679999999999999 6.117 1.284 4.3844662585282403 4.3609999999999998 1.59 2.2269999999999999 3.3069999999999999 1.45 2.4460000000000002 1.63 2.1829999999999998 4.7130000000000001 1.9390000000000001 3.0550000000000002 3.3 2.5870000000000002 1.9 1.794 2.091000000 0000002 2.1349999999999998 2.5 6.9249999999999998 5.431 1.988 1.948 2.1459999999999999 3.2010000000000001 2 4.2699999999999996 2.4089999999999998 3.7989999999999999 2.8580000000000001 2.41 3.05 1.415 1.3120000000000001 1.7569999999999999 2.2040000000000002 1.389 1.4279999999999999 1.5289999999999999 5.282 1.907 3.7629999999999999 3.488 2.6389999999999998 4.6050000000000004 1.5620000000000001 2.34 4.7279999999999998 1.367 1.3720000000000001 1.4770000000000001 4.0410000000000004 6.2830000000000004 2.383 1.504 2.2349999999999999 1.9950000000000001 4.2249999999999996 2.266 3.1739999999999999 1.925 1.536 2.7719999999999998 3.1619999999999999 5.4989999999999997 1.397 1.528 3.8639999999999999 3.7829999999999999 1.6319999999999999 1.909 2.0219999999999998 2.3159999999999998 3.7 5.9009999999999998 1.4830000000000001 1.7070000000000001 1.867 2.077 2.0430000000000001 2.2639999999999998 3.75 2.391 1.75 4.9379999999999997 6.3 3.109
- the logarithmic model (Model 2)
Interpretation of The approximate change in when increases by 1%
Variable Transformation; file UN11
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ln(ppgdp) Residual Plot
6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.31 20368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 1.8106849777263925 -1.3938154881382361 -0.65533572053759448 2.3163554955085583 -0.10098662231564681 -0.18072362277537968 -1.303714187105425 -0.11500079841647204 0.73107192281384159 -1.7617367945772067E-2 -0.50584821781884459 8.0327773261949398E-2 0.50232851785326238 -1.817222998101963 -0.49317391387238563 -1.1678049342509489 0.45264763998237623 -0.11518301205384818 1.1659475211200041 0.84183469447228032 -1.0239869573333529 -7.4341085735734502E-2 -1.6626845072265248 0.13207167582053447 -0.45560241982442284 0.41921795496896053 -1.0325873719231204 1.6178887876833628 -0.75041068107096187 -1.4448047444952734 0.67719399553835391 0.34367309247958855 -0.71753991159189212 0.38130066256384021 0.20269514186927573 1.8133773018674875 -0.35923517625796442 -1.2550559610365053 -0.29960751640367178 0.82617084314620293 1.323572412656099 0.35626570759254328 -0.64822289520559839 0.58660902725046338 -0.59686477042465436 -1.1955439916282029 -0.19399105161015862 -0.40473840555956864 0.76260422367314273 0.65292147211730112 1.7070611995273044E-2 0.48221040510836755 -0.21449988635242612 1.9759485363968858 -0.46248602491035129 -0.48508570517468907 -0.79176410055861934 3.0051681345239158 -7.8960824807481345E-3 -0.38184978848433015 -0.57595999321613167 -0.33939655795044255 0.50229354090355027 0.54108278310341174 0.29445482550881286 1.0333586274490965 0.62399670490260206 -1.5869010627121463 1.5943353899703583E-2 0.44006350029545827 -0.15405970957864579 0.70052567938850396 -0.31174596344382932 0.77015434473179223 0.77878745760049384 0.76795953829813346 -0.85585482602936613 -0.87103025618021057 -0.29238060140356525 -0.44363149120408574 -0.71132937583511491 0.64786777086982017 -0.97679213660585384 -1.0005965184046191 -1.1137278916854976 0.73543066690245773 0.74778968096443288 1.2773800533613917 -6.5858729268853722E-2 -0.478925335948714 2.6036199781548808E-2 8.7812322193507431E-2 0.12858762494617171 0.75976299337629705 1.1874015300394447E-2 0.89110086859821491 -1.1949041638066249 -1.1544271326641669 -0.75265375370570475 -0.58054792661155319 -0.68734696665015704 0.36888870313154687 0.18846583363853675 -0.74574211014650693 0.84315949051802996 -0.13759063328038335 0.23161101419085384 1.6037307547830988 0.16341459866051267 -1.1006878032117122 2.07274013989253 -0.5972014678068216 1.3536200326225956 0.71112655359015609 -0.88781593835256323 -0.1298931327469206 0.19161291246085321 -1.9749001884813231 -0.77832543082439409 -0.93464857387901823 -0.89057872343246292 0.43007702569448991 -1.8692135097029317 0.34200391466820301 0.70412541785918403 -1.5274671925928494 4.1227689907380682E-2 0.45397030032793984 0.57499637206881182 0.56496308936286876 -1.1494350289680764 2.5612510344752373 1.8380253726922859 -2.1631326515859839 0.97355863392771758 0.30140314692129522 -0.52328118943161739 -0.24948712872528755 0.91489784040529987 -5.849344561222658E-2 0.29383265529496816 -0.23624248880275678 -0.26932135761056841 -0.20446779048822439 -0.75695131520413383 -0.51360596241875034 6.1938126187259579E-2 1.1330586455995459 -0.44785515382627072 -1.0469986159208178 -0.74804430121572185 1.1647432845320331 -0.6419138580854522 0.78515644909639182 -8.359105785848131E-2 0.62559033358789984 0.89869006294789866 -1.1511776112974472 0.12553506241179591 0.35376158260003621 -1.5801154964828257E-2 -0.63594789264862128 -0.30203101878641481 0.42442493117037294 1.2145206033373031 -0.11445934298590199 -0.1021060870020718 -0.95481061928252275 -0.60272052733714521 0.87173543799323028 -0.25203694404176691 0.19017405052611869 0.61081532604077737 0.43417304158787617 -0.28735028522512396 -0.69035128963742043 1.3624582955699021 -1.4056960313843956 -1.2502521054854374 -0.26229210506594214 0.84114857653069519 -0.40661533064111821 -0.92413126987820049 -0.27059087707103613 -0.46566247941284278 0.6925066622455871 1.7559886877926356 -1.5548350229485624 0.26231715150867729 0.36843354427473329 0.7321425819172136 -0.14486944336888374 -1.2416450526865703 0.69738184963220107 0.27875481710283267 -1.8722117844792674 1.4366411279464586 2.7060242639127301 -0.96246146814189615ln(ppgdp)
Residuals
fertility
fertility6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825 936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.262636067432773 7 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 5.968 1.5249999999999999 2.1419999999999999 5.1349999999999998 2 2.1720000000000002 1.7350000000000001 1.671 1.9490000000000001 1.3460000000000001 2.1480000000000001 1.877 2.4300000000000002 2.157 1.575 1.4790000000000001 1.835 2.6789999999999998 5.0780000000000003 1.76 2.258 3.2290000000000001 1.1339999999999999 2.617 1.8 1.984 1.546 5.75 4.0510000000000002 2.4220000000000002 4.2869999999999999 1.6910000000000001 2.2789999999999999 1.6 4.423 5.7370000000000001 1.8320000000000001 1.5589999999999999 2.2930000000000001 4.742 4.4420000000000002 2.5308062840941101 1.8120000000000001 4.2240000000000002 1.5009999999999999 1.4510000000000001 1.458 1.5009999999999999 5.4850000000000003 1.885 3.589 3 2.4900000000000002 5.9180000000000001 2.3929999999999998 2.6360000000000001 2.1709999999999998 4.9800000000000004 4.2430000000000003 1.702 3.8479999999999999 2.6019999999999999 1.875 1.9870000000000001 2.0329999999999999 3.1949999999999998 4.6890000000000001 1.528 1.4570000000000001 3.988 1.54 2.2170000000000001 2.1709999999999998 3.84 5.032 4.8769999999999998 2.19 3.1589999999999998 2.996 1.137 1.43 2.0979999999999999 2.5379999999999998 2.0550000000000002 1.587 4.5350000000000001 2.097 2.9089999999999998 1.476 2.262 1.4179999999999999 2.8889999999999998 2.4809999999999999 4.6230000000000002 3.5 2.2509999999999999 2.621 2.5430000000000001 1.506 1.764 3.0510000000000002 5.0380000000000003 2.41 1.4950000000000001 1.6830000000000001 1.163 4.4930000000000003 5.968 2.5720000000000001 1.6679999999999999 6.117 1.284 4.3844662585282403 4.3609999999999998 1.59 2.2269999999999999 3.3069999999999999 1.45 2.4460000000000002 1.63 2.1829999999999998 4.7130000000000001 1.9390000000000001 3.0550000000000002 3.3 2.5870000000000002 1.9 1.794 2.0910000000000002 2.1349999999999998 2.5 6.9249999999999998 5.431 1.988 1.948 2.1459999999999999 3.2010000000000001 2 4.2699999999999996 2.4089999999999998 3.7989999999999999 2.8580000000000001 2.41 3.05 1.415 1.3120000000000001 1.7569999999999999 2.2040000000000002 1.389 1.4279999999999999 1.5289999999999999 5.282 1.907 3.7629999999999999 3.488 2.6389999999999998 4.6050000000000004 1.5620000000000001 2.34 4.7279999999999998 1.367 1.3720000000000001 1.4770000000000001 4.0410000000000004 6.2830000000000004 2.383 1.504 2.2349999999999999 1.9950000000000001 4.2249999999999996 2.266 3.1739999999999999 1.925 1.536 2.7719999999999998 3.1619999999999999 5.4989999999999997 1.397 1.528 3.8639999999999999 3.7829999999999999 1.6319999999999999 1.909 2.0219999999999998 2.3159999999999998 3.7 5.9009999999999998 1.4830000000000001 1.7070000000000001 1.867 2.077 2.0430000000000001 2.2639999999999998 3.75 2.391 1.75 4.9379999999999997 6.3 3.109
– the exponential model (Model 3)
Interpretation of The approximate percent change in when increases by 1
), where
Variable Transformation; file UN11
27
ppgdp Residual Plot
499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 0.73367060008076335 -0.59505905508598511 -0.24637750753361176 0.62626567191123272 -0.21079835644876599 -0.17981548360433197 -0.47330555750360292 -0.28832426852870385 0.25035627141619443 -0.25412209005231912 -0.23050308650933582 -0.17644992185959918 3.3734813192667135E-2 -0.28209825614567874 -0.44130000533176578 -0.60295093608505623 4.0693473089380094E-2 -2.241786930410461E-2 0.57489474535550311 0.54704594069753676 -0.22087716165148064 0.13603769927891252 -0.88231349826434613 -1.3189202619627638E-2 -0.35023307198256248 -6.6317500421754216E-3 -0.55120026358892193 0.6966910309199954 0.34260229311512713 -0.16479914960509856 0.41079151841262118 -1.2440949934485857E-2 -0.19818108904107146 5.2246225830625825E-2 0.43353570145220544 0.69675985129851736 -0.31945003722538601 -0.56540913261592041 -0.15860808717031105 0.50638571951374489 0.46268645634122096 7.3223040091969782E-3 -0.37740783234066022 0.39539735817174559 -0.49703469634572317 -0.62203719647034261 -0.36277801783074581 -0.44067330849353747 0.64592511703502264 0.20249694469232227 0.23393134193755993 0.11910388686277085 -8.7722987243567307E-2 0.72758280336503711 -0.14006573576074244 -5.928366233705018E-2 -0.24469077401483208 0.73631987562126688 0.39174440092088525 -0.36781499863139233 0.29285394391310815 -6.2249689861008095E-2 6.9970805691265681E-2 7.2339759288123862E-2 -7.1825396158602728E-2 0.24325391783311801 0.49337751489099224 -0.60428789859162424 -0.23441223284327745 0.33991576592629524 -0.32895266648590493 0.13410982475022037 -0.19973686009706659 0.31949302190858142 0.56227338780461977 0.5322426628361987 -0.24080107107984761 9.8790988782048839E-2 6.1685630664423785E-2 -0.57260506276483514 -0.55599647237524707 0.12369007430458689 -0.11117575892067222 -0.30495115817251828 -0.53780429897173687 0.4634574 9049485963 0.20116794396453297 0.33860289716571779 -0.28860505851418317 -0.18708457602995809 -0.22467075885274956 5.2481900456297081E-2 -4.6750527870483172E-2 0.4817027033659631 0.2109047883966324 0.26316501909307932 -8.5071057103729197E-2 -0.11323658325105246 -0.52915324942936426 -0.38651448973092783 6.8137120366548176E-2 0.56111932204818893 -5.1597238594529471E-2 -0.53297513012515418 0.64234271266377829 -0.34600497656325369 0.44891361646474359 0.73208058304255696 -1.9643076816582616E-2 -0.49411725610580148 0.75945116504151811 -0.5882861745504534 0.45418948742071041 0.42705793514904489 -0.51052485898166267 -0.15549795394136878 0.16777026390254268 -0.66852494368587601 -0.13866241780378519 -0.49666637220222937 -0.24547352767946884 0.49655593767036121 -0.38633333269851899 0.11598000927766039 0.20508619128829564 -0.10184148667708715 -0.18830632627378563 5.2849182702113695E-2 7.5898249990677846E-2 6.3626316490237866E-2 -0.12934373869032068 0.88081014089466514 0.64770041045449278 -0.36555600991688608 0.55829962416282808 -6.1278092204811951E-2 0.1163836266321685 -0.24368004354608142 0.41370037161582229 -9.3635674591643903E-2 0.29243278253810456 2.2894077368538657E-2 -0.11796136075204189 8.0828131198345199E-2 -0.57351230770806638 -0.5460704172409675 -0.19760787207678798 0.54488062302011031 -0.49336667511018317 -0.61760110465091 -0.5174953876589059 0.61193747455263581 -0.33783645976355081 0.30441370544152546 0.20539409607254289 8.9875830811140589E-2 0.48039428890133906 -0.55484937532923251 -7.9615541109127164E-2 0.49910699532174596 -0.25408840787951575 -0.56268152376897485 -0.40883308097005716 0.35154941785921601 0.78079215420125103 -0.10852063315949445 -0.30725319341970053 -0.22743118610554081 -0.29839883922580779 0.40316644142740876 -0.16152368021440411 0.13382936715671345 0.14574595330793416 0.14428834572541183 -5.8577998162239187E-3 0.10202304800833129 0.65201588658103704 -0.67422271323894112 -0.58258798385762778 0.29924911423704748 0.31195808047146789 -0.39780118166319195 -0.36435527432746506 -0.24090016976244066 -0.16699020691851452 0.28577717690085591 0.72249285459319146 -0.630197623330922 -7.866392047906412E-2 -2.6100400793229506E-2 0.19524087781188915 -0.20971247561943862 -0.22518428315372185 0.29668828472277919 -3.501188677583067E-2 -0.48544825278766268 0.55475411387379725 0.79610430693150014 8.2391932256846045E-2ppgdp
Residuals
ln(ferility)
ln(ferility) 499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 1.7864118629014598 0.42199441005937488 0.76173997202555699 1.6360798433805215 0.69314718055994529 0.77564840207168906 0.55100741339882253 0.51342224961325666 0.66731642052542384 0.2971372312225361 0.76453717664661835 0.62967475760437175 0.88789125735245711 0.76871836740701938 0.45425527227759638 0.39136618372866283 0.60704448150653356 0.98544359056247166 1.6249174832824866 0.56531380905006046 0.81447946572747032 1.1721724917761382 0.12575120530556025 0.96202862354800878 0.58778666490211906 0.68511500886268106 0.43567095016523022 1.7491998548092591 1.3989637642205535 0.88459364513090055 1.4555871876158399 0.52532006991644331 0.8237367502635472 0.47000362924573563 1.48681819888618 97 1.7469364256197339 0.60540826625193855 0.44404459007563946 0.82986100387576744 1.5564589876432138 1.4911047254722358 0.92853794133402046 0.5944312076207876 1.4407825464039603 0.40613155265132483 0.37225297390205087 0.37706563358646639 0.40613155265132483 1.7020170937271937 0.63392782089997413 1.2778736121654701 1.0986122886681098 0.91228271047661635 1.7779985539780179 0.87254780892623618 0.96926261664026081 0.7751878908961547 1.6054298910365616 1.4452705662201879 0.53180403015118238 1.34755353280346 0.95628038009031346 0.62860865942237409 0.68662596356967986 0.70951253464620956 1.161587087829498 1.5452193401074492 0.42395969074432877 0.37637952721306783 1.383289852099592 0.43178241642553783 0.79615493063417442 0.7751878908961547 1.3454723665996355 1.61581 75193981394 1.5845302767279155 0.78390154382840938 1.1502555218199482 1.097278065654973 0.12839321476839899 0.35767444427181588 0.74098450997410537 0.9313763692921958 0.72027584794819799 0.46184544154427198 1.5118250835670999 0.74050775191978291 1.0678093795130645 0.38933572617828072 0.81624937769392869 0.3492474281099357 1.0609104214840981 0.9086617047096639 1.5310438450060884 1.2527629684953681 0.81137456192459512 0.96355592434126924 0.93334448643998269 0.40945712937770185 0.56758395758459956 1.1154694057345327 1.6170091779304185 0.87962674750256364 0.40212620684264982 0.52057791520866903 0.15100287353652742 1.5025206300880229 1.7864118629014598 0.94468380637537297 0.51162530393655492 1.8110717802604279 0.24998020526776946 1.4780678985817615 1.4727013888606293 0.46373401623214022 0.80065538827523053 1.1960414339996557 0.37156355643248301 0.89445403726498074 0.48858001481867092 0.78070007756780679 1.5503246479415937 0.66217237626051473 1.1167795926235586 1.1939224684724346 0.95049890320389219 0.64185388617239469 0.58444776363660444 0.73764242044649664 0.75846664668058783 0.91629073187415511 1.9351380520734023 1.6921232790527083 0.68712910823438234 0.66680320522034331 0.76360564420850674 1.163463260987726 0.69314718055994529 1.451613827240533 0.87921172363273425 1.3347378742054885 1.0501220795076758 0.87962674750256364 1.1151415906193203 0.34712953109520095 0.27155269052189734 0.56360780920496012 0.79027389129066816 0.32858406377220672 0.3562748639173926 0.42461392694692518 1.6643048138749406 0.64553132661828205 1.3252165116113002 1.2493285060467332 0.97040005752118697 1.5271426697072703 0.44596705141749426 0.85015092936961001 1.553502280103797 0.31261855774181252 0.31626952930369356 0.39001300354924279 1.3964921860963366 1.83784757342081 0.86836019811660503 0.4081282255276481 0.80424122806553211 0.69064405034182685 1.441019260809137 0.81801616260581456 1.1549926221042173 0.65492596773974754 0.42918163472548043 1.0195690813276568 1.1512047387872804 1.7045662575256777 0.33432708027482477 0.42395969074432877 1.3517029163502716 1.3305173456508921 0.48980625654191517 0.64657954474361057 0.7040871205982796 0.8398415597107487 1.3083328196501789 1.7751218280750316 0.39406706315579509 0.53473744381230359 0.62433286455958559 0.73092454489397518 0.71441931583548512 0.81713316034093642 1.3217558399823195 0.87171168847618763 0.55961578793542266 1.5969603909229877 1.8405496333974869 1.1343011310766167
– the log-log model (Model 4)
Interpretation of The approximate percent change in when increases by 1%
), where
Variable Transformation; file UN11
28
ln(ppgdp) Residual Plot
6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.3832595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566 445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.0050333446371109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.8929002060614657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.0755552392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 0.40784455052790092 -0.54283247322373751 -0.16250466654320006 0.70471666728028692 1.5290119690146708E-3 -6.6507549398076016E-5 -0.45387353352405002 -7.2969904477447556E-2 0.2706979764430093 -0.1481510330829815 -0.11177318394486224 3.9717643486564924E-2 0.25417176250742846 -0.54868414792307563 -0.22640129019499805 -0.48259125618318177 0.15549749570361471 6.2252164308221669E-2 0.3282840167818124 0.26883587721893898 -0.27167061175699891 7.888872872736874E-2 -0.79827588511939407 0.14214863482991003 -0.15548336518918915 0.17262449092595411 -0.41549733017803653 0.37905227523244367 -0.19477392722961406 -0.3969240974443905 0.25992395369924548 8.5473892507772709E-2 -0.1670552104573807 7.312753343396533E-2 8.7208131955557766E-2 0.44643774371423639 -0.11635886437227561 -0.48578571024578354 -2.5990928284407744E-2 0.25856386191510383 0.45959425184392932 0.2123479067654197 -0.21719554037918076 0.23590411595211158 -0.28444371175972039 -0.50161729398451049 -0.16455843733765496 -0.22026084979815919 0.13467558547477743 0.23258219414074288 9.4863663222713113E-2 0.26775447083487869 1.9051355976275164E-2 0.47134345043225134 -7.1122861885415833E-2 -6.3135843443891004E-2 -0.2043207239981315 0.95595572152516284 3.5441015195993408E-2 -0.15408930707146618 -0.12009076478639757 -1.6090068011292091E-2 0.18028403993942077 0.21384412830956245 0.13897368502954366 0.44970623710019386 0.19749022553638595 -0.60637269135134031 -9.4778557216746828E-2 0.2082951083521829 -0.12389535748305203 0.29980237486767813 -4.3963045575813986E-2 0.3301914585618182 0.20521411816702728 0.22208984761479234 -0.22336484687618707 -0.18579029394527757 8.992089877325915E-3 -0.38939206225361073 -0.34742086152570034 0.26679458296903225 -0.23254597383460707 -0.29024490973217454 -0.430125818261 63576 0.25276839745170498 0.30003239099754841 0.53299059957184181 -0.11549689424761389 -8.9150476454901706E-2 -0.10551041186229326 0.13537897544440858 0.13305077233064977 0.25071796190040652 9.7748876706410304E-2 0.36732843355919531 -0.30095767126857598 -0.29158997623424598 -0.33483224723295835 -0.20539973095347253 -0.12313497703659215 6.7468195869053282E-2 0.14773775827371094 -0.33617950091094345 0.25026562480995496 -0.27323030957928895 8.9185758144570526E-2 0.33870820720063821 0.15030738288540546 -0.40304904309775014 0.47027233942520019 -0.36821524363059799 0.47581536899223642 0.26365298993807706 -0.35376996709978464 2.3547587662120062E-2 0.16554668759545899 -0.7623289544951628 -0.17243329198076429 -0.35793178877606141 -0.23582792114831341 0.12979600531438029 -0.59977203426597092 0.22070994798706778 0.33697912114196926 -0.41375441150628633 3.1151253444757443E-2 0.14703933434420324 0.24144710704154604 0.24422065747338162 -0.29261120674261742 0.48760820406256311 0.50208283385255248 -0.68937288507316674 0.35152536204853446 0.15763854791495036 -7.0442225625999777E-2 -4.8079939466696975E-2 0.34103845582346404 6.5156132858059324E-2 0.17403084559532167 2.6691021956819494E-2 -5.1933197922517937E-3 3.8184727653630901E-2 -0.36819551963553754 -0.3280701972888157 7.5952464258013386E-3 0.44275869519486766 -0.27479679499577225 -0.46028794813455265 -0.32581910398760566 0.2991196147679589 -0.19572404539564148 0.34067036696086506 6.6431581659919692E-2 0.30803836123023565 0.29924076522325804 -0.45016323484933185 0.12062352822809463 0.10246826418642807 -0.13907835513730787 -0.34426757476238146 -0.19405078501904788 0.19856763877674233 0.15489133812783029 4.4294023651141656E-2 -0.11816724459970113 -0.25111588050291644 -0.16691596428366495 0.33105776803600029 -1.2924286137393604E-2 0.16844796224789405 0.22615147954587755 7.1348612337216899E-2 7.7943182542945522E-3 -0.12548459776127596 0.33293860172954837 -0.59170825522088899 -0.49390976328647956 -1.6500698078016907E-2 0.35799494250225949 -0.18097579199479147 -0.28962316529430521 -5.1539490784188291E-2 -7.9167183866154067E-2 0.31388169304699987 0.40066476535591944 -0.610520185024788 6.2367968912100835E-2 0.13396271532446891 0.29190333963216197 -6.2234382901104057E-3 -0.34373345420351176 0.31223005342271026 0.17633241900669205 -0.64019179372311563 0.43752564305704156 0.65017475191810514 -0.2155854387158056ln(ppgdp)
Residuals
ln(ferility)
ln(ferility) 6.2126060957515188 8.2099068719895989 8.405814603432848 8.371450399362784 9.5288013757955436 9.1228306890345792 8.0165488949239982 10.036772039682001 10.952890339124952 10.717940445722775 8.6372137220128131 10.019562463511157 9.8083028648573372 6.5078745491678731 9.5817177041734567 8.6485722694726181 10.687726938832723 8.4108989065983195 6.6081355689573131 11.436311123726746 7.6242282848455787 7.5897909547873637 8.406864800720653 8.9096270943145814 9.2794559026068608 10.393526625111543 8.7585852217871807 6.2532517220143964 5.1738872881698592 6.6811055883386397 7.0955617660066617 10.74421171055257 8.0845624152353039 10.951646544796773 6.1110237821656215 6.5894765325528883 9.383 2595311074911 8.3788502417944919 8.7359752452129662 6.6020450040109653 7.8879968593481156 9.4101825424881262 8.9494689926010018 7.0510760984263587 9.5338359172170968 8.6489930858626121 10.252886591155431 9.8436738518342715 5.3013128755278354 10.930070220601412 7.1566445467147624 8.8566324506408556 8.5555288976818105 6.5597568705223015 8.3120368951164139 7.8837101715776026 8.1390319178354176 9.7322483588722797 6.0616899919974792 9.5564375682769942 5.7825936550804906 8.1734908806863054 10.703282669671836 10.585217301576824 10.113302673639005 9.4309848030892969 6.3614751742317441 7.8936840075385621 10.593055836478793 7.1953373464335844 10.185043397920472 10.471431422668699 8.913146539151807 7.9663438655209271 6.0579542883768145 6.2904574107056295 8.005033344637 1109 6.417875419731609 7.613917396619577 10.367966574201658 9.46374151045109 10.578419844675169 7.2487885269309125 7.9893231330409886 8.5616119099628634 6.7895346475947056 10.741174374503975 10.285738621092536 10.430494548880466 8.4967863816385751 10.672226782034295 8.399602637234107 9.1233326313435779 6.6868592002084064 7.2917924396766809 10.723936763469254 6.7631918277907843 6.9542571126335568 9.2745350840181793 9.1360154532143234 6.888266602398275 5.3872435757424384 9.3343970206381623 9.3034207949921939 11.56262378806705 10.819582265199772 6.0447683191302932 5.878855602725328 9.032743635617944 8.4520144653912421 6.3949276525454728 9.8832440280590692 8.0292373817409946 7.0309458895373353 8.9210970814574466 9.1161066126234367 7.892900206061 4657 7.3937552813124716 7.7172177519234308 8.7810640127644799 7.9603236291488395 6.0100409326809174 6.7755943753797983 8.5418272657079104 8.7307065206370034 6.2817058419546861 9.9194150340855014 10.755979756077155 10.472190498332305 10.385052219700158 7.0316529156383742 5.879694646264972 7.1227053552678186 6.2225762680713688 11.34555596693313 9.9422754797433885 6.9109501698786566 9.2893178971596093 7.5063170170522149 8.937743936942443 7.2643102157202932 7.926999632266674 8.5961337534888447 7.6686078358960952 9.4143581868518975 9.9729016686204481 10.183427229849748 11.189932572428278 9.9547603467135506 8.9256405149628666 9.2448770552464179 6.2772072401787113 8.8064390405316999 8.1147136221484395 7.157190164250415 9.6700347934801432 6.9399320106773583 8.5415345228023956 9.3457974093561873 5.8627785394799368 10.687003177158442 9.6788428750956506 10.048012048968754 7.084645445778885 4.7431914838854663 8.8894185977432674 10.326884257608627 7.7728790242810479 8.7277296056912128 7.5092804699947697 8.8562335561431595 8.1050659404345229 10.797659456791925 11.140124042697861 7.9832695164042695 6.7044143549641069 6.2461067654815627 8.3971701488165067 8.4365903268841382 6.2626360674327737 8.1727573291355231 9.6293861768737905 8.3480879135848998 9.2198054365918818 8.4310904923628254 8.0668980673902784 6.2324480165505225 8.0179667034935989 10.587207940173004 10.500311039860483 10.74819420148998 9.3886873740147259 7.2635398266357232 7.994126281227893 9.5106449444291865 7.075555 2392570715 7.2704520552393639 7.1210908893052611 6.3510602215576917 1.7864118629014598 0.42199441005937488 0.76173997202555699 1.6360798433805215 0.69314718055994529 0.77564840207168906 0.55100741339882253 0.51342224961325666 0.66731642052542384 0.2971372312225361 0.76453717664661835 0.62967475760437175 0.88789125735245711 0.76871836740701938 0.45425527227759638 0.39136618372866283 0.60704448150653356 0.98544359056247166 1.6249174832824866 0.56531380905006046 0.81447946572747032 1.1721724917761382 0.12575120530556025 0.96202862354800878 0.58778666490211906 0.68511500886268106 0.43567095016523022 1.7491998548092591 1.3989637642205535 0.88459364513090055 1.4555871876158399 0.52532006991644331 0.8237367502635472 0.47000362924573563 1.4868181988861897 1.7469364256197339 0.60540826625193855 0.44404459007563946 0.82986100387576744 1.5564589876432138 1.4911047254722358 0.92853794133402046 0.5944312076207876 1.4407825464039603 0.40613155265132483 0.37225297390205087 0.37706563358646639 0.40613155265132483 1.7020170937271937 0.63392782089997413 1.2778736121654701 1.0986122886681098 0.91228271047661635 1.7779985539780179 0.87254780892623618 0.96926261664026081 0.7751878908961547 1.6054298910365616 1.4452705662201879 0.53180403015118238 1.34755353280346 0.95628038009031346 0.62860865942237409 0.68662596356967986 0.70951253464620956 1.161587087829498 1.5452193401074492 0.42395969074432877 0.37637952721306783 1.383289852099592 0.43178241642553783 0.79615493063417442 0.7751878908961547 1.3454723665996355 1.6158175193981394 1.5845302767279155 0.78390154382840938 1.1502555218199482 1.097278065654973 0.12839321476839899 0.35767444427181588 0.74098450997410537 0.9313763692921958 0.72027584794819799 0.46184544154427198 1.5118250835670999 0.74050775191978291 1.0678093795130645 0.38933572617828072 0.81624937769392869 0.3492474281099357 1.0609104214840981 0.9086617047096639 1.5310438450060884 1.2527629684953681 0.81137456192459512 0.96355592434126924 0.93334448643998269 0.40945712937770185 0.56758395758459956 1.1154694057345327 1.6170091779304185 0.87962674750256364 0.40212620684264982 0.52057791520866903 0.15100287353652742 1.5025206300880229 1.7864118629014598 0.94468380637537297 0.51162530393655492 1.8110717802604279 0.24998020526776946 1.4780678985817615 1.4727013888606293 0.46373401623214022 0.80065538827523053 1.1960414339996557 0.37156355643248301 0.89445403726498074 0.48858001481867092 0.78070007756780679 1.5503246479415937 0.66217237626051473 1.1167795926235586 1.1939224684724346 0.95049890320389219 0.64185388617239469 0.58444776363660444 0.73764242044649664 0.75846664668058783 0.91629073187415511 1.9351380520734023 1.6921232790527083 0.68712910823438234 0.66680320522034331 0.76360564420850674 1.163463260987726 0.69314718055994529 1.451613827240533 0.87921172363273425 1.3347378742054885 1.0501220795076758 0.87962674750256364 1.1151415906193203 0.34712953109520095 0.27155269052189734 0.56360780920496012 0.79027389129066816 0.32858406377220672 0.3562748639173926 0.42461392694692518 1.6643048138749406 0.64553132661828205 1.3252165116113002 1.2493285060467332 0.97040005752118697 1.5271426697072703 0.44596705141749426 0.85015092936961001 1.553502280103797 0.31261855774181252 0.31626952930369356 0.39001300354924279 1.3964921860963366 1.83784757342081 0.86836019811660503 0.4081282255276481 0.80424122806553211 0.69064405034182685 1.441019260809137 0.81801616260581456 1.1549926221042173 0.65492596773974754 0.42918163472548043 1.0195690813276568 1.1512047387872804 1.7045662575256777 0.33432708027482477 0.42395969074432877 1.3517029163502716 1.3305173456508921 0.48980625654191517 0.64657954474361057 0.7040871205982796 0.8398415597107487 1.3083328196501789 1.7751218280750316 0.39406706315579509 0.53473744381230359 0.62433286455958559 0.73092454489397518 0.71441931583548512 0.81713316034093642 1.3217558399823195 0.87171168847618763 0.55961578793542266 1.5969603909229877 1.8405496333974869 1.1343011310766167
Model 1: ,
Model 2: ,
Model 3: ,
), where
Model 4: ,
), where
Variable Transformation; file UN11
Model 2 is better than Model 1 and Model 4 is better than Model 3. Because of the difference in Y, Models 2 are 4 are not directly comparable. To compare them, we can redefine for Model 4, and represent it as , where and . We have , and . Therefore, Model 4 is better than Model 2.
29
A linear regression model with more than one independent variable is called a multiple linear regression model.
Multiple Linear Regression
Note: The error term ε is assumed to be normally distributed with
a zero mean and a constant unknown standard deviation σ.
30
We estimate the regression coefficients β0, β1, β2,…, βk by finding b0, b1, b2,… bk, then we use the estimated regression equation:
The estimated regression coefficient bj (j = 1,2,...,k) represents the expected change in the dependent variable Y when the associated independent variable Xj is increased by one unit while the values of all other independent variables are held constant.
Estimated Multiple Regression Equation
31
ANOVA Table for Multiple Regression
The general form of the Anova table for the multiple regression:
Degrees of Sum of
Source Freedom Squares Mean Square F
Regression k =
Residual n – k – 1 RSS RMS =
Total n – 1 TSS
k = the number of independent variables
n = the number of observations
TSS = total sum of squares = + RSS
R2 = /TSS = multiple coefficient of determination
RMS = the residual mean square (a point estimate of the unknown
variance 2 of the error term )
s = = standard error of the estimate (a point estimate of the standard deviation )
32
The F statistic for testing the overall significance of the regression model:
is assumed to have the F distribution with df1 = k in the numerator and df2 = n – k – 1 in the denominator. If the null hypothesis is rejected, the regression model is significant (at least one of is significant)
The linear regression output also provides information to test hypotheses, against , about significance of each individual independent variable . The test statistic is assumed to have the t distribution with df = n – k – 1. If we reject , then is significant.
Testing for Significance
33
Example: Adding House Age to Predict Market Value
Although House Age is found insignificant, both adjusted R Square and Standard Error improve.
34
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.7455 | |||||
| R Square | 0.5558 | |||||
| Adjusted R Square | 0.5330 | |||||
| Standard Error | 7211.8485 | |||||
| Observations | 42 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 2 | 2537650171 | 1268825085 | 24.3954 | 0.0000 | |
| Residual | 39 | 2028419591 | 52010758.75 | |||
| Total | 41 | 4566069762 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 47331.38154 | 13884.34664 | 3.408974347 | 0.0015 | 19247.6396 | 75415.1234 |
| House Age | -825.1612203 | 607.3128421 | -1.358708664 | 0.1820 | -2053.5674 | 403.2450 |
| Square Feet | 40.91106845 | 6.696523994 | 6.109299165 | 0.0000 | 27.3661 | 54.4561 |
Predict student graduation rates using several indicators:
Example 8.12: Interpreting Regression Results for the Colleges and Universities Data
35
Regression model
The value of R2 indicates that 53.44% of the variation in Graduation% is explained by the four independent variables.
All independent variables are statistically significant at α = 0.05.
Example 8.12 Continued
36
A good regression model should include only significant independent variables.
However, it is not always clear exactly what will happen when we add or remove variables from a model; variables that are (or are not) significant in one model may (or may not) be significant in another.
Therefore, you should not consider dropping all insignificant variables at one time, but rather take a more structured approach.
Adding an independent variable to a regression model will always result in R2 equal to or greater than the R2 of the original model.
Adjusted R2 reflects both the number of independent variables and the sample size and may either increase or decrease when an independent variable is added or dropped. An increase in adjusted R2 indicates that the model has improved.
Standard Error (the estimate of ) may also increase or decrease when an independent variable is added or dropped. A decrease in Standard Error indicates that the model has improved
Model Building Issues
37
Construct a model with all available independent variables. Check for significance of the independent variables by examining the p-values.
Identify the independent variable having the largest p-value that exceeds the chosen level of significance.
Remove the variable identified in step 2 from the model and evaluate adjusted R2 and Standard Error
(Don’t remove all variables with p-values that exceed α at the same time, but remove only one at a time.)
In general, continue until all variables are significant and/or adjusted R2 and Standard Error cannot be improved.
Systematic Model Building Approach
38
Banking Data (Predicting Customer Average Bank Balance)
Example 8.13: Identifying the Best Regression Model
Home Value has the largest p-value; drop and re-run the regression.
39
Banking Data regression after removing Home Value
Example 8.13 Continued
Adjusted R2 and Standard Error improve. All X variables are significant.
40
Income and Wealth are highly correlated!
Remove one of them.
Multicollinearity occurs when there are strong correlations among the independent variables, and they can predict each other better than the dependent variable.
When significant multicollinearity is present, it becomes difficult to isolate the effect of one independent variable on the dependent variable, the signs of coefficients may be the opposite of what they should be, making it difficult to interpret regression coefficients, and p-values can be inflated.
Correlations exceeding ±0.7 may indicate multicollinearity
The variance inflation factor () computed, for every independent variable , by some software is a better indicator. Any or indicate serious problems.
Multicollinearity
41
Colleges and Universities correlation matrix; none exceed the recommended threshold of ±0.7
Banking Data correlation matrix; large correlations exist
Example 8.14: Identifying Potential Multicollinearity
42
If we remove Wealth from the model, adjusted R2 = 0.9201 and s = 2458, but we discover that Education is no longer significant.
Dropping Education and leaving only Age and Income in the model results in adjusted R2 = 0.9202 and s = 2457.
However, if we remove Income from the model instead of Wealth, adjusted R2 = 0.9345, s = 2226, and all remaining variables (Age, Education, and Wealth) are significant:
Example 8.14 Continued
43
The regression analysis tool in XLMiner has some advanced options not available in Regression tool of Data Analysis of Excel.
Best-subsets regression evaluates either all possible regression models for a set of independent variables or the best subsets of models for a fixed number of independent variables.
Advanced Techniques for Regression Modeling using XLMiner
44
In XLMiner regression models are evaluated by minimizing Mallow’s statistic Cp.
Backward Elimination begins with all independent variables in the model and deletes one at a time until the best model is identified.
Forward Selection begins with a model having no independent variables and successively adds one at a time until no additional variable makes a significant contribution.
Stepwise Selection is similar to Forward Selection except that at each step, the procedure considers dropping variables that are not statistically significant.
Sequential Replacement replaces variables sequentially, retaining those that improve performance. These options might terminate with a different model.
Exhaustive Search looks at all combinations of variables to find the one with the best fit, but it can be time consuming for large numbers of variables.
Best-Subsets Procedures
45
Click the Predict button in the Data Mining group and choose Multiple Linear Regression.
Enter the range of the data (including headers)
Move the appropriate variables to the boxes on the right.
Example 8.19: Using XLMiner for Regression on the file: Banking Data
46
Select the output options and check the Summary report box. Before clicking Finish, click on the Best subsets button.
Select the best subsets option:
Example 8.19 Continued
47
Regression output (all variables):
Best subsets results:
Example 8.19 Continued
The strongly correlated Income and Wealth are kept together!
If you click “Choose Subset,” XLMiner will create a new worksheet
with the results for this model.
48
Identifying the best regression model often requires experimentation and trial and error.
The independent variables selected should make sense in attempting to explain the dependent variable
Logic should guide your model development. In many applications, behavioral, economic, or physical theory might suggest that certain variables should belong in a model.
Additional variables increase R2 and, therefore, help to explain a larger proportion of the variation.
Even though a variable with a large p-value is not statistically significant, it could simply be the result of sampling error and a modeler might wish to keep it.
Good models are as simple as possible (the principle of parsimony).
Practical Issues in Regression Modeling
49
Regression analysis requires numerical data.
Categorical data can be included as independent variables, but must be coded numeric using dummy variables.
For categorical variables with 2 levels, one dummy variable (coded as 0 or 1), is needed.
For categorical variables with m levels, m - 1 dummy variables are needed.
Regression with Categorical Variables
50
Employee Salaries provides data for 35 employees
Predict Salary using Age and MBA (coded as yes=1, no=0)
Example 8.15: A Model with Categorical Variables
51
= 893.59 + 1044.15(Age) + 14767.23(MBA)
If MBA = 0, = 893.59 + 1044.15(Age)
If MBA = 1, =(893.59 +14,767.23) + 1044.15(Age) = 15,660.82 + 1044.15(Age)
Example 8.15 Continued
52
=$14767.23 = the estimated difference between salaries
of those with MBA and without MBA
An interaction occurs when the effect of one variable, say , is dependent on another variable, say .
We can test for interactions by defining a new variable as the product of the two variables, , and testing whether this variable () is significant. This leads to an alternative model:
Interactions
53
Define an interaction between Age and MBA and re-run the regression.
Example 8.16: Incorporating Interaction Terms in a Regression Model
The MBA variable becomes insignificant; drop it and re-run.
54
Adjusted R2 slightly increased, Standard Error slightly decreased, and both Age and the interaction term are significant. The final model is
= 3,323.11 + 984.25(Age) + 425.58(MBA × Age)
Example 8.16 Continued
55
Example 8.17: A Regression Model with Multiple Levels of Categorical Variables
The Excel file Surface Finish provides measurements of the surface finish of 35 parts produced on a lathe, along with the revolutions per minute (RPM) of the spindle and one of four types of cutting tools used.
56
Because we have a continuous independent variable RPM, and a categorical independent variable Cutting Tool with m = 4 levels, we define a regression model of the form:
Example 8.17 Continued
57
Note. There are m – 1 dummies defined.
Add 3 columns to the data, one for each of the three tool type variables
Dummy variables can be created in XLMiner by using Transform > Transform Categorical Data > Create Dummies
Example 8.17 Continued
58
Regression results:
Example 8.17 Continued
59
= 24.49 + 0.098 RPM - 13.31 Type B - 20.49 Type C - 26.04 Type D
Curvilinear models may be appropriate when scatter charts or residual plots show nonlinear relationships.
A second order polynomial might be used
Here β1 represents the linear effect of X on Y and β2 represents the curvilinear effect.
This model is linear in the β parameters so we can use linear regression methods.
Regression Models with Nonlinear Terms
60
The U-shape of the residual plot (a second-order polynomial trendline was fit to the residual data) suggests that a linear relationship is not appropriate.
Example 8.18: Modeling Beverage Sales Using Curvilinear Regression
61
Add a variable for temperature squared.
The estimated regression equation is:
= 142,850.34 - 3,643.17(Temperature) + 23.30(Temperature)2
Example 8.18 Continued
62
Regression Statistics
Multiple R0.439989
R Square0.19359
Adjusted R Square0.189497
Standard Error1.206005
Observations199
ANOVA
dfSSMSFSignificance F
Regression168.7847768.7847747.292727.9E-11
Residual197286.52621.454447
Total198355.3109
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept3.1779120.10477330.331463.69E-762.9712913.384532
ppgdp-3.2E-054.65E-06-6.876977.9E-11-4.1E-05-2.3E-05
UNdata
| region | group | fertility | ppgdp | lifeExpF | pctUrban | |
| Afghanistan | Asia | other | 5.968 | 499 | 49.49 | 23 |
| Albania | Europe | other | 1.525 | 3677.2 | 80.4 | 53 |
| Algeria | Africa | africa | 2.142 | 4473 | 75 | 67 |
| Angola | Africa | africa | 5.135 | 4321.9 | 53.17 | 59 |
| Anguilla | Caribbean | other | 2 | 13750.1 | 81.1 | 100 |
| Argentina | Latin Amer | other | 2.172 | 9162.1 | 79.89 | 93 |
| Armenia | Asia | other | 1.735 | 3030.7 | 77.33 | 64 |
| Aruba | Caribbean | other | 1.671 | 22851.5 | 77.75 | 47 |
| Australia | Oceania | oecd | 1.949 | 57118.9 | 84.27 | 89 |
| Austria | Europe | oecd | 1.346 | 45158.8 | 83.55 | 68 |
| Azerbaijan | Asia | other | 2.148 | 5637.6 | 73.66 | 52 |
| Bahamas | Caribbean | other | 1.877 | 22461.6 | 78.85 | 84 |
| Bahrain | Asia | other | 2.43 | 18184.1 | 76.06 | 89 |
| Bangladesh | Asia | other | 2.157 | 670.4 | 70.23 | 29 |
| Barbados | Caribbean | other | 1.575 | 14497.3 | 80.26 | 45 |
| Belarus | Europe | other | 1.479 | 5702 | 76.37 | 75 |
| Belgium | Europe | oecd | 1.835 | 43814.8 | 82.81 | 97 |
| Belize | Latin Amer | other | 2.679 | 4495.8 | 77.81 | 53 |
| Benin | Africa | africa | 5.078 | 741.1 | 58.66 | 42 |
| Bermuda | Caribbean | other | 1.76 | 92624.7 | 82.3 | 100 |
| Bhutan | Asia | other | 2.258 | 2047.2 | 69.84 | 35 |
| Bolivia | Latin Amer | other | 3.229 | 1977.9 | 69.4 | 67 |
| Bosnia and Herzegovina | Europe | other | 1.134 | 4477.7 | 78.4 | 49 |
| Botswana | Africa | africa | 2.617 | 7402.9 | 51.34 | 62 |
| Brazil | Latin Amer | other | 1.8 | 10715.6 | 77.41 | 87 |
| Brunei Darussalam | Asia | other | 1.984 | 32647.6 | 80.64 | 76 |
| Bulgaria | Europe | other | 1.546 | 6365.1 | 77.12 | 72 |
| Burkina Faso | Africa | africa | 5.75 | 519.7 | 57.02 | 27 |
| Burundi | Africa | africa | 4.051 | 176.6 | 52.58 | 11 |
| Cambodia | Asia | other | 2.422 | 797.2 | 65.1 | 20 |
| Cameroon | Africa | africa | 4.287 | 1206.6 | 53.56 | 59 |
| Canada | North America | oecd | 1.691 | 46360.9 | 83.49 | 81 |
| Cape Verde | Africa | africa | 2.279 | 3244 | 77.7 | 62 |
| Cayman Islands | Caribbean | other | 1.6 | 57047.9 | 83.8 | 100 |
| Central African Republic | Africa | africa | 4.423 | 450.8 | 51.3 | 39 |
| Chad | Africa | africa | 5.737 | 727.4 | 51.61 | 28 |
| Chile | Latin Amer | oecd | 1.832 | 11887.7 | 82.35 | 89 |
| China | Asia | other | 1.559 | 4354 | 75.61 | 48 |
| Colombia | Latin Amer | other | 2.293 | 6222.8 | 77.69 | 75 |
| Comoros | Africa | africa | 4.742 | 736.6 | 63.18 | 28 |
| Congo | Africa | africa | 4.442 | 2665.1 | 59.33 | 63 |
| Cook Islands | Oceania | other | 2.5308062841 | 12212.1 | 76.2454672362 | 76 |
| Costa Rica | Latin Amer | other | 1.812 | 7703.8 | 81.99 | 65 |
| Cote dIvoire | Africa | africa | 4.224 | 1154.1 | 57.71 | 51 |
| Croatia | Europe | other | 1.501 | 13819.5 | 80.37 | 58 |
| Cuba | Caribbean | other | 1.451 | 5704.4 | 81.33 | 75 |
| Cyprus | Asia | other | 1.458 | 28364.3 | 82.14 | 71 |
| Czech Republic | Europe | oecd | 1.501 | 18838.8 | 81 | 74 |
| Democratic Republic of the Congo | Africa | africa | 5.485 | 200.6 | 50.56 | 36 |
| Denmark | Europe | oecd | 1.885 | 55830.2 | 81.37 | 87 |
| Djibouti | Africa | africa | 3.589 | 1282.6 | 60.04 | 76 |
| Dominica | Caribbean | other | 3 | 7020.8 | 78.2 | 67 |
| Dominican Republic | Caribbean | other | 2.49 | 5195.4 | 76.57 | 70 |
| East Timor | Asia | other | 5.918 | 706.1 | 64.2 | 29 |
| Ecuador | Latin Amer | other | 2.393 | 4072.6 | 78.91 | 68 |
| Egypt | Africa | africa | 2.636 | 2653.7 | 75.52 | 44 |
| El Salvador | Latin Amer | other | 2.171 | 3425.6 | 77.09 | 65 |
| Equatorial Guinea | Africa | africa | 4.98 | 16852.4 | 52.91 | 40 |
| Eritrea | Africa | africa | 4.243 | 429.1 | 64.41 | 22 |
| Estonia | Europe | oecd | 1.702 | 14135.4 | 79.95 | 70 |
| Ethiopia | Africa | africa | 3.848 | 324.6 | 61.59 | 17 |
| Fiji | Oceania | other | 2.602 | 3545.7 | 72.27 | 52 |
| Finland | Europe | oecd | 1.875 | 44501.7 | 83.28 | 85 |
| France | Europe | oecd | 1.987 | 39545.9 | 84.9 | 86 |
| French Polynesia | Oceania | other | 2.033 | 24669 | 78.07 | 51 |
| Gabon | Africa | africa | 3.195 | 12468.8 | 64.32 | 86 |
| Gambia | Africa | africa | 4.689 | 579.1 | 60.3 | 59 |
| Georgia | Asia | other | 1.528 | 2680.3 | 77.31 | 53 |
| Germany | Europe | oecd | 1.457 | 39857.1 | 82.99 | 74 |
| Ghana | Africa | africa | 3.988 | 1333.2 | 65.8 | 52 |
| Greece | Europe | oecd | 1.54 | 26503.8 | 82.58 | 62 |
| Greenland | NorthAtlantic | other | 2.217 | 35292.7 | 71.6 | 84 |
| Grenada | Caribbean | other | 2.171 | 7429 | 77.72 | 40 |
| Guatemala | Latin Amer | other | 3.84 | 2882.3 | 75.1 | 50 |
| Guinea | Africa | africa | 5.032 | 427.5 | 56.39 | 36 |
| Guinea-Bissau | Africa | africa | 4.877 | 539.4 | 50.4 | 30 |
| Guyana | Latin Amer | other | 2.19 | 2996 | 73.45 | 29 |
| Haiti | Caribbean | other | 3.159 | 612.7 | 63.87 | 54 |
| Honduras | Latin Amer | other | 2.996 | 2026.2 | 75.92 | 52 |
| Hong Kong | Asia | other | 1.137 | 31823.7 | 86.35 | 100 |
| Hungary | Europe | oecd | 1.43 | 12884 | 78.47 | 68 |
| Iceland | Europe | other | 2.098 | 39278 | 83.77 | 94 |
| India | Asia | other | 2.538 | 1406.4 | 67.62 | 30 |
| Indonesia | Asia | other | 2.055 | 2949.3 | 71.8 | 45 |
| Iran | Asia | other | 1.587 | 5227.1 | 75.28 | 71 |
| Iraq | Asia | other | 4.535 | 888.5 | 72.6 | 66 |
| Ireland | Europe | oecd | 2.097 | 46220.3 | 83.17 | 62 |
| Israel | Asia | oecd | 2.909 | 29311.6 | 84.19 | 92 |
| Italy | Europe | oecd | 1.476 | 33877.1 | 84.62 | 69 |
| Jamaica | Caribbean | other | 2.262 | 4899 | 75.98 | 52 |
| Japan | Asia | oecd | 1.418 | 43140.9 | 87.12 | 67 |
| Jordan | Asia | other | 2.889 | 4445.3 | 75.17 | 79 |
| Kazakhstan | Asia | other | 2.481 | 9166.7 | 72.84 | 59 |
| Kenya | Africa | africa | 4.623 | 801.8 | 59.16 | 23 |
| Kiribati | Oceania | other | 3.5 | 1468.2 | 63.1 | 44 |
| Kuwait | Asia | other | 2.251 | 45430.4 | 75.89 | 98 |
| Kyrgyzstan | Asia | other | 2.621 | 865.4 | 72.36 | 35 |
| Laos | Asia | other | 2.543 | 1047.6 | 69.42 | 34 |
| Latvia | Europe | other | 1.506 | 10663 | 78.51 | 68 |
| Lebanon | Asia | other | 1.764 | 9283.7 | 75.07 | 87 |
| Lesotho | Africa | africa | 3.051 | 980.7 | 48.11 | 28 |
| Liberia | Africa | africa | 5.038 | 218.6 | 58.59 | 48 |
| Libya | Africa | africa | 2.41 | 11320.8 | 77.86 | 78 |
| Lithuania | Europe | other | 1.495 | 10975.5 | 78.28 | 67 |
| Luxembourg | Europe | oecd | 1.683 | 105095.4 | 82.67 | 85 |
| Macao | Asia | other | 1.163 | 49990.2 | 83.8 | 100 |
| Madagascar | Africa | africa | 4.493 | 421.9 | 68.61 | 31 |
| Malawi | Africa | africa | 5.968 | 357.4 | 55.17 | 20 |
| Malaysia | Asia | other | 2.572 | 8372.8 | 76.86 | 73 |
| Maldives | Asia | other | 1.668 | 4684.5 | 78.7 | 41 |
| Mali | Africa | africa | 6.117 | 598.8 | 53.14 | 37 |
| Malta | Europe | other | 1.284 | 19599.2 | 82.29 | 95 |
| Marshall Islands | Oceania | other | 4.3844662585 | 3069.4 | 70.6 | 72 |
| Mauritania | Africa | africa | 4.361 | 1131.1 | 60.95 | 42 |
| Mauritius | Africa | africa | 1.59 | 7488.3 | 76.89 | 42 |
| Mexico | Latin Amer | oecd | 2.227 | 9100.7 | 79.64 | 78 |
| Micronesia | Oceania | other | 3.307 | 2678.2 | 70.17 | 23 |
| Moldova | Europe | other | 1.45 | 1625.8 | 73.48 | 48 |
| Mongolia | Asia | other | 2.446 | 2246.7 | 72.83 | 63 |
| Montenegro | Europe | other | 1.63 | 6509.8 | 77.37 | 61 |
| Morocco | Africa | africa | 2.183 | 2865 | 74.86 | 59 |
| Mozambique | Africa | africa | 4.713 | 407.5 | 51.81 | 39 |
| Myanmar | Asia | other | 1.939 | 876.2 | 67.87 | 34 |
| Namibia | Africa | africa | 3.055 | 5124.7 | 63.04 | 39 |
| Nauru | Oceania | other | 3.3 | 6190.1 | 57.1 | 100 |
| Nepal | Asia | other | 2.587 | 534.7 | 70.05 | 19 |
| Neth Antilles | Caribbean | other | 1.9 | 20321.1 | 79.86 | 93 |
| Netherlands | Europe | oecd | 1.794 | 46909.7 | 82.79 | 83 |
| New Caledonia | Oceania | other | 2.091 | 35319.5 | 80.49 | 57 |
| New Zealand | Oceania | oecd | 2.135 | 32372.1 | 82.77 | 86 |
| Nicaragua | Latin Amer | other | 2.5 | 1131.9 | 77.45 | 58 |
| Niger | Africa | africa | 6.925 | 357.7 | 55.77 | 17 |
| Nigeria | Africa | africa | 5.431 | 1239.8 | 53.38 | 51 |
| North Korea | Asia | other | 1.988 | 504 | 72.12 | 60 |
| Norway | Europe | oecd | 1.948 | 84588.7 | 83.47 | 80 |
| Oman | Asia | other | 2.146 | 20791 | 76.44 | 73 |
| Pakistan | Asia | other | 3.201 | 1003.2 | 66.88 | 36 |
| Palau | Oceania | other | 2 | 10821.8 | 72.1 | 84 |
| Palestinian Territory | Asia | other | 4.27 | 1819.5 | 74.81 | 74 |
| Panama | Latin Amer | other | 2.409 | 7614 | 79.07 | 75 |
| Papua New Guinea | Oceania | other | 3.799 | 1428.4 | 65.52 | 13 |
| Paraguay | Latin Amer | other | 2.858 | 2771.1 | 74.91 | 62 |
| Peru | Latin Amer | other | 2.41 | 5410.7 | 76.9 | 77 |
| Philippines | Asia | other | 3.05 | 2140.1 | 72.57 | 49 |
| Poland | Europe | oecd | 1.415 | 12263.2 | 80.56 | 61 |
| Portugal | Europe | oecd | 1.312 | 21437.6 | 82.76 | 61 |
| Puerto Rico | Caribbean | other | 1.757 | 26461 | 83.2 | 99 |
| Qatar | Asia | other | 2.204 | 72397.9 | 78.24 | 96 |
| Republic of Korea | Asia | other | 1.389 | 21052.2 | 83.95 | 83 |
| Romania | Europe | other | 1.428 | 7522.4 | 77.95 | 58 |
| Russian Federation | Europe | other | 1.529 | 10351.4 | 75.01 | 73 |
| Rwanda | Africa | africa | 5.282 | 532.3 | 57.13 | 19 |
| Saint Lucia | Caribbean | other | 1.907 | 6677.1 | 77.54 | 28 |
| Samoa | Oceania | other | 3.763 | 3343.3 | 76.02 | 20 |
| Sao Tome and Principe | Africa | africa | 3.488 | 1283.3 | 66.48 | 63 |
| Saudi Arabia | Asia | other | 2.639 | 15835.9 | 75.57 | 82 |
| Senegal | Africa | africa | 4.605 | 1032.7 | 60.92 | 43 |
| Serbia | Europe | other | 1.562 | 5123.2 | 77.05 | 56 |
| Seychelles | Africa | africa | 2.34 | 11450.6 | 78 | 56 |
| Sierra Leone | Africa | africa | 4.728 | 351.7 | 48.87 | 39 |
| Singapore | Asia | other | 1.367 | 43783.1 | 83.71 | 100 |
| Slovakia | Europe | oecd | 1.372 | 15976 | 79.53 | 55 |
| Slovenia | Europe | oecd | 1.477 | 23109.8 | 82.84 | 49 |
| Solomon Islands | Oceania | other | 4.041 | 1193.5 | 70 | 19 |
| Somalia | Africa | africa | 6.283 | 114.8 | 53.38 | 38 |
| South Africa | Africa | africa | 2.383 | 7254.8 | 54.09 | 62 |
| Spain | Europe | other | 1.504 | 30542.8 | 84.76 | 78 |
| Sri Lanka | Asia | other | 2.235 | 2375.3 | 78.4 | 14 |
| St Vincent and Grenadines | Caribbean | other | 1.995 | 6171.7 | 74.73 | 50 |
| Sudan | Africa | africa | 4.225 | 1824.9 | 63.82 | 41 |
| Suriname | Latin Amer | other | 2.266 | 7018 | 74.18 | 70 |
| Swaziland | Africa | africa | 3.174 | 3311.2 | 48.54 | 21 |
| Sweden | Europe | oecd | 1.925 | 48906.2 | 83.65 | 85 |
| Switzerland | Europe | oecd | 1.536 | 68880.2 | 84.71 | 74 |
| Syria | Asia | other | 2.772 | 2931.5 | 77.72 | 56 |
| Tajikistan | Asia | other | 3.162 | 816 | 71.23 | 26 |
| Tanzania | Africa | africa | 5.499 | 516 | 60.31 | 27 |
| TFYR Macedonia | Europe | other | 1.397 | 4434.5 | 77.14 | 59 |
| Thailand | Asia | other | 1.528 | 4612.8 | 77.76 | 34 |
| Togo | Africa | africa | 3.864 | 524.6 | 59.4 | 44 |
| Tonga | Oceania | other | 3.783 | 3543.1 | 75.38 | 24 |
| Trinidad and Tobago | Caribbean | other | 1.632 | 15205.1 | 73.82 | 14 |
| Tunisia | Africa | africa | 1.909 | 4222.1 | 77.05 | 68 |
| Turkey | Asia | oecd | 2.022 | 10095.1 | 76.61 | 70 |
| Turkmenistan | Asia | other | 2.316 | 4587.5 | 69.4 | 50 |
| Tuvalu | Oceania | other | 3.7 | 3187.2 | 65.1 | 51 |
| Uganda | Africa | africa | 5.901 | 509 | 55.44 | 13 |
| Ukraine | Europe | other | 1.483 | 3035 | 74.58 | 69 |
| United Arab Emirates | Asia | other | 1.707 | 39624.7 | 78.02 | 84 |
| United Kingdom | Europe | oecd | 1.867 | 36326.8 | 82.42 | 80 |
| United States | North America | oecd | 2.077 | 46545.9 | 81.31 | 83 |
| Uruguay | Latin Amer | other | 2.043 | 11952.4 | 80.66 | 93 |
| Uzbekistan | Asia | other | 2.264 | 1427.3 | 71.9 | 36 |
| Vanuatu | Oceania | other | 3.75 | 2963.5 | 73.58 | 26 |
| Venezuela | Latin Amer | other | 2.391 | 13502.7 | 77.73 | 94 |
| Viet Nam | Asia | other | 1.75 | 1182.7 | 77.44 | 31 |
| Yemen | Asia | other | 4.938 | 1437.2 | 67.66 | 32 |
| Zambia | Africa | africa | 6.3 | 1237.8 | 50.04 | 36 |
| Zimbabwe | Africa | africa | 3.109 | 573.1 | 52.72 | 39 |
Ferility-ppgdp
| ppgdp | fertility | SUMMARY OUTPUT | ||||||||||
| Afghanistan | 499 | 5.968 | ||||||||||
| Albania | 3677.2 | 1.525 | Regression Statistics | |||||||||
| Algeria | 4473 | 2.142 | Multiple R | 0.439989055 | ||||||||
| Angola | 4321.9 | 5.135 | R Square | 0.1935903686 | ||||||||
| Anguilla | 13750.1 | 2 | Adjusted R Square | 0.1894969186 | ||||||||
| Argentina | 9162.1 | 2.172 | Standard Error | 1.2060047574 | ||||||||
| Armenia | 3030.7 | 1.735 | Observations | 199 | ||||||||
| Aruba | 22851.5 | 1.671 | ||||||||||
| Australia | 57118.9 | 1.949 | ANOVA | |||||||||
| Austria | 45158.8 | 1.346 | df | SS | MS | F | Significance F | |||||
| Azerbaijan | 5637.6 | 2.148 | Regression | 1 | 68.7847730399 | 68.7847730399 | 47.2927171482 | 0.0000000001 | ||||
| Bahamas | 22461.6 | 1.877 | Residual | 197 | 286.5261525659 | 1.454447475 | ||||||
| Bahrain | 18184.1 | 2.43 | Total | 198 | 355.3109256058 | |||||||
| Bangladesh | 670.4 | 2.157 | ||||||||||
| Barbados | 14497.3 | 1.575 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Belarus | 5702 | 1.479 | Intercept | 3.1779116422 | 0.1047727783 | 30.3314629275 | 3.69486423775359E-76 | 2.9712914427 | 3.3845318417 | 2.9712914427 | 3.3845318417 | |
| Belgium | 43814.8 | 1.835 | ppgdp | -0.0000320112 | 0.0000046548 | -6.8769700558 | 0.0000000001 | -0.0000411909 | -0.0000228315 | -0.0000411909 | -0.0000228315 | |
| Belize | 4495.8 | 2.679 | ||||||||||
| Benin | 741.1 | 5.078 | ||||||||||
| Bermuda | 92624.7 | 1.76 | ||||||||||
| Bhutan | 2047.2 | 2.258 | RESIDUAL OUTPUT | PROBABILITY OUTPUT | ||||||||
| Bolivia | 1977.9 | 3.229 | ||||||||||
| Bosnia and Herzegovina | 4477.7 | 1.134 | Observation | Predicted fertility | Residuals | Percentile | fertility | |||||
| Botswana | 7402.9 | 2.617 | 1 | 3.1619380468 | 2.8060619532 | 0.2512562814 | 1.134 | |||||
| Brazil | 10715.6 | 1.8 | 2 | 3.0602000087 | -1.5352000087 | 0.7537688442 | 1.137 | |||||
| Brunei Darussalam | 32647.6 | 1.984 | 3 | 3.0347254851 | -0.8927254851 | 1.256281407 | 1.163 | |||||
| Bulgaria | 6365.1 | 1.546 | 4 | 3.0395623795 | 2.0954376205 | 1.7587939698 | 1.284 | |||||
| Burkina Faso | 519.7 | 5.75 | 5 | 2.7377542583 | -0.7377542583 | 2.2613065327 | 1.312 | |||||
| Burundi | 176.6 | 4.051 | 6 | 2.8846217049 | -0.7126217049 | 2.7638190955 | 1.346 | |||||
| Cambodia | 797.2 | 2.422 | 7 | 3.0808952581 | -1.3458952581 | 3.2663316583 | 1.367 | |||||
| Cameroon | 1206.6 | 4.287 | 8 | 2.4464074017 | -0.7754074017 | 3.7688442211 | 1.372 | |||||
| Canada | 46360.9 | 1.691 | 9 | 1.3494663513 | 0.5995336487 | 4.2713567839 | 1.389 | |||||
| Cape Verde | 3244 | 2.279 | 10 | 1.7323236634 | -0.3863236634 | 4.7738693467 | 1.397 | |||||
| Cayman Islands | 57047.9 | 1.6 | 11 | 2.9974452261 | -0.8494452261 | 5.2763819095 | 1.415 | |||||
| Central African Republic | 450.8 | 4.423 | 12 | 2.4588885737 | -0.5818885737 | 5.7788944724 | 1.418 | |||||
| Chad | 727.4 | 5.737 | 13 | 2.5958165386 | -0.1658165386 | 6.2814070352 | 1.428 | |||||
| Chile | 11887.7 | 1.832 | 14 | 3.1564513248 | -0.9994513248 | 6.783919598 | 1.43 | |||||
| China | 4354 | 1.559 | 15 | 2.7138354797 | -1.1388354797 | 7.2864321608 | 1.45 | |||||
| Colombia | 6222.8 | 2.293 | 16 | 2.995383704 | -1.516383704 | 7.7889447236 | 1.451 | |||||
| Comoros | 736.6 | 4.742 | 17 | 1.7753467341 | 0.0596532659 | 8.2914572864 | 1.457 | |||||
| Congo | 2665.1 | 4.442 | 18 | 3.0339956295 | -0.3549956295 | 8.7939698492 | 1.458 | |||||
| Cook Islands | 12212.1 | 2.5308062841 | 19 | 3.154188132 | 1.923811868 | 9.2964824121 | 1.476 | |||||
| Costa Rica | 7703.8 | 1.812 | 20 | 0.2128826145 | 1.5471173855 | 9.7989949749 | 1.477 | |||||
| Cote dIvoire | 1154.1 | 4.224 | 21 | 3.1123782863 | -0.8543782863 | 10.3015075377 | 1.479 | |||||
| Croatia | 13819.5 | 1.501 | 22 | 3.1145966634 | 0.1144033366 | 10.8040201005 | 1.483 | |||||
| Cuba | 5704.4 | 1.451 | 23 | 3.0345750324 | -1.9005750324 | 11.3065326633 | 1.495 | |||||
| Cyprus | 28364.3 | 1.458 | 24 | 2.9409358313 | -0.3239358313 | 11.8090452261 | 1.501 | |||||
| Czech Republic | 18838.8 | 1.501 | 25 | 2.8348922851 | -1.0348922851 | 12.3115577889 | 1.501 | |||||
| Democratic Republic of the Congo | 200.6 | 5.485 | 26 | 2.1328223551 | -0.1488223551 | 12.8140703518 | 1.504 | |||||
| Denmark | 55830.2 | 1.885 | 27 | 2.9741570685 | -1.4281570685 | 13.3165829146 | 1.506 | |||||
| Djibouti | 1282.6 | 3.589 | 28 | 3.1612754146 | 2.5887245854 | 13.8190954774 | 1.525 | |||||
| Dominica | 7020.8 | 3 | 29 | 3.1722584619 | 0.8787415381 | 14.3216080402 | 1.528 | |||||
| Dominican Republic | 5195.4 | 2.49 | 30 | 3.152392303 | -0.730392303 | 14.824120603 | 1.528 | |||||
| East Timor | 706.1 | 5.918 | 31 | 3.1392869122 | 1.1477130878 | 15.3266331658 | 1.529 | |||||
| Ecuador | 4072.6 | 2.393 | 32 | 1.6938429839 | -0.0028429839 | 15.8291457286 | 1.536 | |||||
| Egypt | 2653.7 | 2.636 | 33 | 3.0740672663 | -0.7950672663 | 16.3316582915 | 1.54 | |||||
| El Salvador | 3425.6 | 2.171 | 34 | 1.3517391475 | 0.2482608525 | 16.8341708543 | 1.546 | |||||
| Equatorial Guinea | 16852.4 | 4.98 | 35 | 3.1634809872 | 1.2595190128 | 17.3366834171 | 1.559 | |||||
| Eritrea | 429.1 | 4.243 | 36 | 3.1546266856 | 2.5823733144 | 17.8391959799 | 1.562 | |||||
| Estonia | 14135.4 | 1.702 | 37 | 2.797371942 | -0.965371942 | 18.3417085427 | 1.575 | |||||
| Ethiopia | 324.6 | 3.848 | 38 | 3.0385348195 | -1.4795348195 | 18.8442211055 | 1.587 | |||||
| Fiji | 3545.7 | 2.602 | 39 | 2.9787122641 | -0.6857122641 | 19.3467336683 | 1.59 | |||||
| Finland | 44501.7 | 1.875 | 40 | 3.1543321825 | 1.5876678175 | 19.8492462312 | 1.6 | |||||
| France | 39545.9 | 1.987 | 41 | 3.0925985577 | 1.3494014423 | 20.351758794 | 1.63 | |||||
| French Polynesia | 24669 | 2.033 | 42 | 2.7869875044 | -0.2561812203 | 20.8542713568 | 1.632 | |||||
| Gabon | 12468.8 | 3.195 | 43 | 2.9313036572 | -1.1193036572 | 21.3567839196 | 1.668 | |||||
| Gambia | 579.1 | 4.689 | 44 | 3.1409675009 | 1.0830324991 | 21.8592964824 | 1.671 | |||||
| Georgia | 2680.3 | 1.528 | 45 | 2.7355326801 | -1.2345326801 | 22.3618090452 | 1.683 | |||||
| Germany | 39857.1 | 1.457 | 46 | 2.9953068771 | -1.5443068771 | 22.864321608 | 1.691 | |||||
| Ghana | 1333.2 | 3.988 | 47 | 2.269935985 | -0.811935985 | 23.3668341709 | 1.702 | |||||
| Greece | 26503.8 | 1.54 | 48 | 2.5748587972 | -1.0738587972 | 23.8693467337 | 1.707 | |||||
| Greenland | 35292.7 | 2.217 | 49 | 3.1714901928 | 2.3135098072 | 24.3718592965 | 1.735 | |||||
| Grenada | 7429 | 2.171 | 50 | 1.3907192019 | 0.4942807981 | 24.8743718593 | 1.75 | |||||
| Guatemala | 2882.3 | 3.84 | 51 | 3.13685406 | 0.45214594 | 25.3768844221 | 1.757 | |||||
| Guinea | 427.5 | 5.032 | 52 | 2.9531673159 | 0.0468326841 | 25.8793969849 | 1.76 | |||||
| Guinea-Bissau | 539.4 | 4.877 | 53 | 3.0116005847 | -0.5216005847 | 26.3819095477 | 1.764 | |||||
| Guyana | 2996 | 2.19 | 54 | 3.1553085245 | 2.7626914755 | 26.8844221106 | 1.794 | |||||
| Haiti | 612.7 | 3.159 | 55 | 3.0475427749 | -0.6545427749 | 27.3869346734 | 1.8 | |||||
| Honduras | 2026.2 | 2.996 | 56 | 3.0929634855 | -0.4569634855 | 27.8894472362 | 1.812 | |||||
| Hong Kong | 31823.7 | 1.137 | 57 | 3.0682540299 | -0.8972540299 | 28.391959799 | 1.832 | |||||
| Hungary | 12884 | 1.43 | 58 | 2.6384458713 | 2.3415541287 | 28.8944723618 | 1.835 | |||||
| Iceland | 39278 | 2.098 | 59 | 3.1641756306 | 1.0788243694 | 29.3969849246 | 1.867 | |||||
| India | 1406.4 | 2.538 | 60 | 2.7254203378 | -1.0234203378 | 29.8994974874 | 1.875 | |||||
| Indonesia | 2949.3 | 2.055 | 61 | 3.1675208024 | 0.6804791976 | 30.4020100503 | 1.877 | |||||
| Iran | 5227.1 | 1.587 | 62 | 3.0644094832 | -0.4624094832 | 30.9045226131 | 1.885 | |||||
| Iraq | 888.5 | 4.535 | 63 | 1.7533582317 | 0.1216417683 | 31.4070351759 | 1.9 | |||||
| Ireland | 46220.3 | 2.097 | 64 | 1.9119994025 | 0.0750005975 | 31.9095477387 | 1.907 | |||||
| Israel | 29311.6 | 2.909 | 65 | 2.3882270215 | -0.3552270215 | 32.4120603015 | 1.909 | |||||
| Italy | 33877.1 | 1.476 | 66 | 2.7787702259 | 0.4162297741 | 32.9145728643 | 1.925 | |||||
| Jamaica | 4899 | 2.262 | 67 | 3.1593739486 | 1.5296260514 | 33.4170854271 | 1.939 | |||||
| Japan | 43140.9 | 1.418 | 68 | 3.0921119872 | -1.5641119872 | 33.9195979899 | 1.948 | |||||
| Jordan | 4445.3 | 2.889 | 69 | 1.9020375129 | -0.4450375129 | 34.4221105528 | 1.949 | |||||
| Kazakhstan | 9166.7 | 2.481 | 70 | 3.1352342926 | 0.8527657074 | 34.9246231156 | 1.984 | |||||
| Kenya | 801.8 | 4.623 | 71 | 2.3294928474 | -0.7894928474 | 35.4271356784 | 1.987 | |||||
| Kiribati | 1468.2 | 3.5 | 72 | 2.0481494949 | 0.1688505051 | 35.9296482412 | 1.988 | |||||
| Kuwait | 45430.4 | 2.251 | 73 | 2.9401003387 | -0.7691003387 | 36.432160804 | 1.995 | |||||
| Kyrgyzstan | 865.4 | 2.621 | 74 | 3.0856457221 | 0.7543542779 | 36.9346733668 | 2 | |||||
| Laos | 1047.6 | 2.543 | 75 | 3.1642268485 | 1.8677731515 | 37.4371859296 | 2 | |||||
| Latvia | 10663 | 1.506 | 76 | 3.1606447937 | 1.7163552063 | 37.9396984925 | 2.022 | |||||
| Lebanon | 9283.7 | 1.764 | 77 | 3.0820060472 | -0.8920060472 | 38.4422110553 | 2.033 | |||||
| Lesotho | 980.7 | 3.051 | 78 | 3.1582983718 | 0.0007016282 | 38.9447236181 | 2.043 | |||||
| Liberia | 218.6 | 5.038 | 79 | 3.1130505218 | -0.1170505218 | 39.4472361809 | 2.055 | |||||
| Libya | 11320.8 | 2.41 | 80 | 2.1591963938 | -1.0221963938 | 39.9497487437 | 2.077 | |||||
| Lithuania | 10975.5 | 1.495 | 81 | 2.7654791702 | -1.3354791702 | 40.4522613065 | 2.091 | |||||
| Luxembourg | 105095.4 | 1.683 | 82 | 1.9205752065 | 0.1774247935 | 40.9547738693 | 2.097 | |||||
| Macao | 49990.2 | 1.163 | 83 | 3.1328910718 | -0.5948910718 | 41.4572864322 | 2.098 | |||||
| Madagascar | 421.9 | 4.493 | 84 | 3.0835009708 | -1.0285009708 | 41.959798995 | 2.135 | |||||
| Malawi | 357.4 | 5.968 | 85 | 3.0105858292 | -1.4235858292 | 42.4623115578 | 2.142 | |||||
| Malaysia | 8372.8 | 2.572 | 86 | 3.1494696792 | 1.3855303208 | 42.9648241206 | 2.146 | |||||
| Maldives | 4684.5 | 1.668 | 87 | 1.6983437605 | 0.3986562395 | 43.4673366834 | 2.148 | |||||
| Mali | 598.8 | 6.117 | 88 | 2.2396117627 | 0.6693882373 | 43.9698492462 | 2.157 | |||||
| Malta | 19599.2 | 1.284 | 89 | 2.0934645684 | -0.6174645684 | 44.472361809 | 2.171 | |||||
| Marshall Islands | 3069.4 | 4.3844662585 | 90 | 3.0210887083 | -0.7590887083 | 44.9748743719 | 2.171 | |||||
| Mauritania | 1131.1 | 4.361 | 91 | 1.7969190907 | -0.3789190907 | 45.4773869347 | 2.172 | |||||
| Mauritius | 7488.3 | 1.59 | 92 | 3.0356121958 | -0.1466121958 | 45.9798994975 | 2.183 | |||||
| Mexico | 9100.7 | 2.227 | 93 | 2.8844744533 | -0.4034744533 | 46.4824120603 | 2.19 | |||||
| Micronesia | 2678.2 | 3.307 | 94 | 3.1522450514 | 1.4707549486 | 46.9849246231 | 2.204 | |||||
| Moldova | 1625.8 | 1.45 | 95 | 3.1309127788 | 0.3690872212 | 47.4874371859 | 2.217 | |||||
| Mongolia | 2246.7 | 2.446 | 96 | 1.7236294179 | 0.5273705821 | 47.9899497487 | 2.227 | |||||
| Montenegro | 6509.8 | 1.63 | 97 | 3.1502091382 | -0.5292091382 | 48.4924623116 | 2.235 | |||||
| Morocco | 2865 | 2.183 | 98 | 3.1443766951 | -0.6013766951 | 48.9949748744 | 2.251 | |||||
| Mozambique | 407.5 | 4.713 | 99 | 2.8365760749 | -1.3305760749 | 49.4974874372 | 2.258 | |||||
| Myanmar | 876.2 | 1.939 | 100 | 2.8807291414 | -1.1167291414 | 50 | 2.262 | |||||
| Namibia | 5124.7 | 3.055 | 101 | 3.1465182453 | -0.0955182453 | 50.5025125628 | 2.264 | |||||
| Nauru | 6190.1 | 3.3 | 102 | 3.170913991 | 1.867086009 | 51.0050251256 | 2.266 | |||||
| Nepal | 534.7 | 2.587 | 103 | 2.8155190988 | -0.4055190988 | 51.5075376884 | 2.279 | |||||
| Neth Antilles | 20321.1 | 1.9 | 104 | 2.8265725707 | -1.3315725707 | 52.0100502513 | 2.293 | |||||
| Netherlands | 46909.7 | 1.794 | 105 | -0.1863196231 | 1.8693196231 | 52.5125628141 | 2.316 | |||||
| New Caledonia | 35319.5 | 2.091 | 106 | 1.5776646875 | -0.4146646875 | 53.0150753769 | 2.34 | |||||
| New Zealand | 32372.1 | 2.135 | 107 | 3.1644061113 | 1.3285938887 | 53.5175879397 | 2.383 | |||||
| Nicaragua | 1131.9 | 2.5 | 108 | 3.1664708346 | 2.8015291654 | 54.0201005025 | 2.391 | |||||
| Niger | 357.7 | 6.925 | 109 | 2.9098881555 | -0.3378881555 | 54.5226130653 | 2.393 | |||||
| Nigeria | 1239.8 | 5.431 | 110 | 3.0279551135 | -1.3599551135 | 55.0251256281 | 2.409 | |||||
| North Korea | 504 | 1.988 | 111 | 3.1587433277 | 2.9582566723 | 55.527638191 | 2.41 | |||||
| Norway | 84588.7 | 1.948 | 112 | 2.5505174707 | -1.2665174707 | 56.0301507538 | 2.41 | |||||
| Oman | 20791 | 2.146 | 113 | 3.0796564241 | 1.3048098344 | 56.5326633166 | 2.422 | |||||
| Pakistan | 1003.2 | 3.201 | 114 | 3.1417037588 | 1.2192962412 | 57.0351758794 | 2.43 | |||||
| Palau | 10821.8 | 2 | 115 | 2.9382020737 | -1.3482020737 | 57.5376884422 | 2.446 | |||||
| Palestinian Territory | 1819.5 | 4.27 | 116 | 2.8865871934 | -0.6595871934 | 58.040201005 | 2.481 | |||||
| Panama | 7614 | 2.409 | 117 | 3.0921792108 | 0.2148207892 | 58.5427135678 | 2.49 | |||||
| Papua New Guinea | 1428.4 | 3.799 | 118 | 3.1258678116 | -1.6758678116 | 59.0452261307 | 2.5 | |||||
| Paraguay | 2771.1 | 2.858 | 119 | 3.1059920493 | -0.6599920493 | 59.5477386935 | 2.5308062841 | |||||
| Peru | 5410.7 | 2.41 | 120 | 2.9695250459 | -1.3395250459 | 60.0502512563 | 2.538 | |||||
| Philippines | 2140.1 | 3.05 | 121 | 3.0861995161 | -0.9031995161 | 60.5527638191 | 2.543 | |||||
| Poland | 12263.2 | 1.415 | 122 | 3.1648670728 | 1.5481329272 | 61.0552763819 | 2.572 | |||||
| Portugal | 21437.6 | 1.312 | 123 | 3.1498634171 | -1.2108634171 | 61.5577889447 | 2.587 | |||||
| Puerto Rico | 26461 | 1.757 | 124 | 3.0138637774 | 0.0411362226 | 62.0603015075 | 2.602 | |||||
| Qatar | 72397.9 | 2.204 | 125 | 2.9797590308 | 0.3202409692 | 62.5628140704 | 2.617 | |||||
| Republic of Korea | 21052.2 | 1.389 | 126 | 3.1607952464 | -0.5737952464 | 63.0653266332 | 2.621 | |||||
| Romania | 7522.4 | 1.428 | 127 | 2.5274085758 | -0.6274085758 | 63.567839196 | 2.636 | |||||
| Russian Federation | 10351.4 | 1.529 | 128 | 1.6762752301 | 0.1177247699 | 64.0703517588 | 2.639 | |||||
| Rwanda | 532.3 | 5.282 | 129 | 2.0472915944 | 0.0437084056 | 64.5728643216 | 2.679 | |||||
| Saint Lucia | 6677.1 | 1.907 | 130 | 2.1416414444 | -0.0066414444 | 65.0753768844 | 2.772 | |||||
| Samoa | 3343.3 | 3.763 | 131 | 3.1416781499 | -0.6416781499 | 65.5778894472 | 2.858 | |||||
| Sao Tome and Principe | 1283.3 | 3.488 | 132 | 3.1664612312 | 3.7585387688 | 66.0804020101 | 2.889 | |||||
| Saudi Arabia | 15835.9 | 2.639 | 133 | 3.13822414 | 2.29277586 | 66.5829145729 | 2.909 | |||||
| Senegal | 1032.7 | 4.605 | 134 | 3.1617779907 | -1.1737779907 | 67.0854271357 | 2.996 | |||||
| Serbia | 5123.2 | 1.562 | 135 | 0.4701247245 | 1.4778752755 | 67.5879396985 | 3 | |||||
| Seychelles | 11450.6 | 2.34 | 136 | 2.5123665067 | -0.3663665067 | 68.0904522613 | 3.05 | |||||
| Sierra Leone | 351.7 | 4.728 | 137 | 3.145797993 | 0.055202007 | 68.5929648241 | 3.051 | |||||
| Singapore | 43783.1 | 1.367 | 138 | 2.8314926942 | -0.8314926942 | 69.0954773869 | 3.055 | |||||
| Slovakia | 15976 | 1.372 | 139 | 3.1196672396 | 1.1503327604 | 69.5979899497 | 3.109 | |||||
| Slovenia | 23109.8 | 1.477 | 140 | 2.9341782642 | -0.5251782642 | 70.1005025126 | 3.159 | |||||
| Solomon Islands | 1193.5 | 4.041 | 141 | 3.1321868251 | 0.6668131749 | 70.6030150754 | 3.162 | |||||
| Somalia | 114.8 | 6.283 | 142 | 3.089205369 | -0.231205369 | 71.1055276382 | 3.174 | |||||
| South Africa | 7254.8 | 2.383 | 143 | 3.0047085704 | -0.5947085704 | 71.608040201 | 3.195 | |||||
| Spain | 30542.8 | 1.504 | 144 | 3.1094044446 | -0.0594044446 | 72.1105527638 | 3.201 | |||||
| Sri Lanka | 2375.3 | 2.235 | 145 | 2.7853517314 | -1.3703517314 | 72.6130653266 | 3.229 | |||||
| St Vincent and Grenadines | 6171.7 | 1.995 | 146 | 2.4916680561 | -1.1796680561 | 73.1155778894 | 3.3 | |||||
| Sudan | 1824.9 | 4.225 | 147 | 2.3308629273 | -0.5738629273 | 73.6180904523 | 3.307 | |||||
| Suriname | 7018 | 2.266 | 148 | 0.8603670235 | 1.3436329765 | 74.1206030151 | 3.488 | |||||
| Swaziland | 3311.2 | 3.174 | 149 | 2.5040051777 | -1.1150051777 | 74.6231155779 | 3.5 | |||||
| Sweden | 48906.2 | 1.925 | 150 | 2.9371104913 | -1.5091104913 | 75.1256281407 | 3.589 | |||||
| Switzerland | 68880.2 | 1.536 | 151 | 2.8465507689 | -1.3175507689 | 75.6281407035 | 3.7 | |||||
| Syria | 2931.5 | 2.772 | 152 | 3.1608720734 | 2.1211279266 | 76.1306532663 | 3.75 | |||||
| Tajikistan | 816 | 3.162 | 153 | 2.9641695699 | -1.0571695699 | 76.6331658291 | 3.763 | |||||
| Tanzania | 516 | 5.499 | 154 | 3.0708885528 | 0.6921114472 | 77.135678392 | 3.783 | |||||
| TFYR Macedonia | 4434.5 | 1.397 | 155 | 3.1368316522 | 0.3511683478 | 77.6381909548 | 3.799 | |||||
| Thailand | 4612.8 | 1.528 | 156 | 2.6709852696 | -0.0319852696 | 78.1407035176 | 3.84 | |||||
| Togo | 524.6 | 3.864 | 157 | 3.1448536622 | 1.4601463378 | 78.6432160804 | 3.848 | |||||
| Tonga | 3543.1 | 3.783 | 158 | 3.0139117943 | -1.4519117943 | 79.1457286432 | 3.864 | |||||
| Trinidad and Tobago | 15205.1 | 1.632 | 159 | 2.8113640433 | -0.4713640433 | 79.648241206 | 3.988 | |||||
| Tunisia | 4222.1 | 1.909 | 160 | 3.1666532985 | 1.5613467015 | 80.1507537688 | 4.041 | |||||
| Turkey | 10095.1 | 2.022 | 161 | 1.7763614895 | -0.4093614895 | 80.6532663317 | 4.051 | |||||
| Turkmenistan | 4587.5 | 2.316 | 162 | 2.6665004987 | -1.2945004987 | 81.1557788945 | 4.224 | |||||
| Tuvalu | 3187.2 | 3.7 | 163 | 2.4381389053 | -0.9611389053 | 81.6582914573 | 4.225 | |||||
| Uganda | 509 | 5.901 | 164 | 3.1397062591 | 0.9012937409 | 82.1608040201 | 4.243 | |||||
| Ukraine | 3035 | 1.483 | 165 | 3.1742367549 | 3.1087632451 | 82.6633165829 | 4.27 | |||||
| United Arab Emirates | 39624.7 | 1.707 | 166 | 2.945676692 | -0.562676692 | 83.1658291457 | 4.287 | |||||
| United Kingdom | 36326.8 | 1.867 | 167 | 2.2001995569 | -0.6961995569 | 83.6683417085 | 4.361 | |||||
| United States | 46545.9 | 2.077 | 168 | 3.1018754073 | -0.8668754073 | 84.1708542714 | 4.3844662585 | |||||
| Uruguay | 11952.4 | 2.043 | 169 | 2.9803480371 | -0.9853480371 | 84.6733668342 | 4.423 | |||||
| Uzbekistan | 1427.3 | 2.264 | 170 | 3.1194943791 | 1.1055056209 | 85.175879397 | 4.442 | |||||
| Vanuatu | 2963.5 | 3.75 | 171 | 2.9532569473 | -0.6872569473 | 85.6783919598 | 4.493 | |||||
| Venezuela | 13502.7 | 2.391 | 172 | 3.0719161127 | 0.1020838873 | 86.1809045226 | 4.535 | |||||
| Viet Nam | 1182.7 | 1.75 | 173 | 1.6123648427 | 0.3126351573 | 86.6834170854 | 4.605 | |||||
| Yemen | 1437.2 | 4.938 | 174 | 0.9729728685 | 0.5630271315 | 87.1859296482 | 4.623 | |||||
| Zambia | 1237.8 | 6.3 | 175 | 3.0840707704 | -0.3120707704 | 87.6884422111 | 4.689 | |||||
| Zimbabwe | 573.1 | 3.109 | 176 | 3.1517904921 | 0.0102095079 | 88.1909547739 | 4.713 | |||||
| 177 | 3.1613938561 | 2.3376061439 | 88.6934673367 | 4.728 | ||||||||
| 178 | 3.0359579169 | -1.6389579169 | 89.1959798995 | 4.742 | ||||||||
| 179 | 3.0302503175 | -1.5022503175 | 89.6984924623 | 4.877 | ||||||||
| 180 | 3.1611185597 | 0.7028814403 | 90.2010050251 | 4.938 | ||||||||
| 181 | 3.0644927124 | 0.7185072876 | 90.7035175879 | 4.98 | ||||||||
| 182 | 2.691177943 | -1.059177943 | 91.2060301508 | 5.032 | ||||||||
| 183 | 3.0427570986 | -1.1337570986 | 91.7085427136 | 5.038 | ||||||||
| 184 | 2.8547552429 | -0.8327552429 | 92.2110552764 | 5.078 | ||||||||
| 185 | 3.0310602012 | -0.7150602012 | 92.7135678392 | 5.135 | ||||||||
| 186 | 3.0758855032 | 0.6241144968 | 93.216080402 | 5.282 | ||||||||
| 187 | 3.1616179346 | 2.7393820654 | 93.7185929648 | 5.431 | ||||||||
| 188 | 3.0807576099 | -1.5977576099 | 94.2211055276 | 5.485 | ||||||||
| 189 | 1.9094769189 | -0.2024769189 | 94.7236180905 | 5.499 | ||||||||
| 190 | 2.0150466992 | -0.1480466992 | 95.2261306533 | 5.737 | ||||||||
| 191 | 1.6879209095 | 0.3890790905 | 95.7286432161 | 5.75 | ||||||||
| 192 | 2.7953008165 | -0.7523008165 | 96.2311557789 | 5.901 | ||||||||
| 193 | 3.1322220375 | -0.8682220375 | 96.7336683417 | 5.918 | ||||||||
| 194 | 3.0830464116 | 0.6669535884 | 97.2361809045 | 5.968 | ||||||||
| 195 | 2.7456738325 | -0.3546738325 | 97.7386934673 | 5.968 | ||||||||
| 196 | 3.1400519802 | -1.3900519802 | 98.2412060302 | 6.117 | ||||||||
| 197 | 3.1319051265 | 1.8060948735 | 98.743718593 | 6.283 | ||||||||
| 198 | 3.1382881624 | 3.1617118376 | 99.2462311558 | 6.3 | ||||||||
| 199 | 3.1595660159 | -0.0505660159 | 99.7487437186 | 6.925 |
ppgdp Residual Plot
499 3677.2 4473 4321.8999999999996 13750.1 9162.1 3030.7 22851.5 57118.9 45158.8 5637.6 22461.599999999999 18184.099999999999 670.4 14497.3 5702 43814.8 4495.8 741.1 92624.7 2047.2 1977.9 4477.7 7402.9 10715.6 32647.599999999999 6365.1 519.70000000000005 176.6 797.2 1206.5999999999999 46360.9 3244 57047.9 450.8 727.4 11887.7 4354 6222.8 736.6 2665.1 12212.1 7703.8 1154.0999999999999 13819.5 5704.4 28364.3 18838.8 200.6 55830.2 1282.5999999999999 7020.8 5195.3999999999996 706.1 4072.6 2653.7 3425.6 16852.400000000001 429.1 14135.4 324.60000000000002 3545.7 44501.7 39545.9 24669 12468.8 579.1 2680.3 39857.1 1333.2 26503.8 35292.699999999997 7429 2882.3 427.5 539.4 2996 612.70000000000005 2026.2 31823.7 12884 39278 1406.4 2949.3 5227.1000000000004 888.5 46220.3 29311.599999999999 33877.1 4899 43140.9 4445.3 9166.7000000000007 801.8 1468.2 45430.400000000001 865.4 1047.5999999999999 10663 9283.7000000000007 980.7 218.6 11320.8 10975.5 105095.4 49990.2 421.9 357.4 8372.7999999999993 4684.5 598.79999999999995 19599.2 3069.4 1131.0999999999999 7488.3 9100.7000000000007 2678.2 1625.8 2246.6999999999998 6509.8 2865 407.5 876.2 5124.7 6190.1 534.70000000000005 20321.099999999999 46909.7 35319.5 32372.1 1131.9000000000001 357.7 1239.8 504 84588.7 20791 1003.2 10821.8 1819.5 7614 1428.4 2771.1 5410.7 2140.1 12263.2 21437.599999999999 26461 72397.899999999994 21052.2 7522.4 10351.4 532.29999999999995 6677.1 3343.3 1283.3 15835.9 1032.7 5123.2 11450.6 351.7 43783.1 15976 23109.8 1193.5 114.8 7254.8 30542.799999999999 2375.3000000000002 6171.7 1824.9 7018 3311.2 48906.2 68880.2 2931.5 816 516 4434.5 4612.8 524.6 3543.1 15205.1 4222.1000000000004 10095.1 4587.5 3187.2 509 3035 39624.699999999997 36326.800000000003 46545.9 11952.4 1427.3 2963.5 13502.7 1182.7 1437.2 1237.8 573.1 2.8060619532387685 -1.5352000086793103 -0.89272548514221617 2.0954376205294913 -0.73775425831892294 -0.71262170489870202 -1.3458952580720365 -0.77540740167088429 0.59953364866214143 -0.38632366342129698 -0.84944522614334694 -0.58188857373310232 -0.16581653858598022 -0.99945132480312893 -1.1388354797477789 -1.5163837040073971 5.965326591540232E-2 -0.35499562947917829 1.9238118679765552 1.5471173855349225 -0.85437828634387891 0.11440333657504498 -1.9005750324397477 -0.32393583132048676 -1.0348922850509064 -0.14882235514948672 -1.4281570684740383 2.5887245853538952 0.87874153807370314 -0.73039230295781143 1.1477130877635835 -2.8429839240102783E-3 -0.79506726627703506 0.24826085251846997 1.2595190127581355 2.5823733143544665 -0.96537194195235387 -1.4795348195238625 -0.68571226412536834 1.5876678175167451 1.3494014423487206 -0.25618122026659584 -1.1193036572411807 1.0830324990657987 -1.2345326801165175 -1.5443068770954986 -0.81193598503945341 -1.073858797244267 2.3135098071926907 0.49428079809384085 0.45214593997371066 4.6832684080966303E-2 -0.521600 5846606917 2.7626914755113652 -0.65454277494399138 -0.45696348548279841 -0.89725402994336312 2.3415541286742005 1.0788243694297179 -1.0234203378378446 0.68047919764079268 -0.46240948322709619 0.12164176832509033 7.500059749682797E-2 -0.35522702151422614 0.41622977409113115 1.5296260514233895 -1.5641119872092539 -0.44503751292696747 0.85276570736624269 -0.78949284736763081 0.16885050512692468 -0.76910033865358818 0.75435427787555742 1.8677731514884517 1.7163552062557308 -0.89200604717323939 7.0162818997188126E-4 -0.11705052182299269 -1.0221963937800616 -1.335479170150385 0.17742479345612971 -0.59489107182084533 -1.0285009708339357 -1.4235858291993628 1.3855303208156702 0.39865623948725459 0.66938823731124941 -0.617464568408022 -0.75908870828018804 -0.37891909072150143 -0.14661219575038098 -0.40347445331756315 1.4707549486233278 0.3690872211605476 0.5273705821085779 -0.52920913821135551 -0.6013766951497086 -1.3305760748700208 -1.1167291413624987 -9.5518245318886308E-2 1.8670860090319312 -0.40551909876710468 -1.3315725707165376 1.8693196231248199 -0.41466468752645325 1.3285938886940216 2.801529165436742 -0.33788815554940399 -1.3599551135311387 2.9582566723252248 -1.2665174706576792 1.3048098344105714 1.219296241160102 -1.3482020737054226 -0.65958719339477856 0.21482078924283465 -1.6758678116247678 -0.65999204929229505 -1.3395250459108095 -0.90319951611437954 1.5481329272226287 -1.2108634171078112 4.1136222559623903E-2 0.32024096920001099 -0.57379524644673729 -0.62740857578280096 0.11772476993017067 4.3708405643127612E-2 -6.6414444111977389E-3 -0. 64167814986926475 3.7585387688007295 2.2927758600448498 -1.1737779906947758 1.4778752755272708 -0.36636650665729142 5.520200698016442E-2 -0.83149269419938676 1.1503327603897269 -0.52517826419472602 0.66681317487155978 -0.23120536904241806 -0.59470857043910819 -5.9404444629131525E-2 -1.3703517313615285 -1.179668056143236 -0.57386292729649191 1.343632976537565 -1.1150051777456438 -1.5091104913321947 -1.3175507689315422 2.1211279266413636 -1.0571695699272006 0.69211144720277584 0.35116834782301476 -3.1985269636250369E-2 1.4601463377722537 -1.4519117942603128 -0.47136404328191395 1.5613467015209825 -0.40936148954592722 -1.2945004986541606 -0.96113890527778145 0.90129374086947012 3.1087632450923106 -0.56267669200890547 -0.69619955688469126 -0.86687540726305379 -0.98534803712454577 1.1055056209414991 -0.68725694731624909 0.10208388725612982 0.31263515726594426 0.56302713154329975 -0.31207077043051834 1.0209507852061872E-2 2.3376061438647175 -1.6389579168539254 -1.5022503175241138 0.70288144029902178 0.7185072876183467 -1.0591779429803052 -1.1337570985569647 -0.83275524289806269 -0.71506020122038016 0.62411449680802811 2.7393820653716801 -1.5977576098548845 -0.20247691889582975 -0.14804669920870106 0.38907909053485179 -0.75230081645241675 -0.86822203746306048 0.66695358839479857 -0.35467383248715256 -1.3900519802340745 1.8060948735485218 3.1617118376182671 -5.0566015856357449E-2ppgdp
Residuals
Normal Probability Plot
0.25125628140703515 0.75376884422110546 1.2562814070351758 1.7587939698492461 2.2613065326633164 2.7638190954773867 3.266331658291457 3.7688442211055273 4.2713567839195976 4.7738693467336679 5.2763819095477382 5.7788944723618085 6.2814070351758788 6.7839195979899491 7.2864321608040195 7.7889447236180898 8.2914572864321592 8.7939698492462313 9.2964824120602998 9.7989949748743719 10.30150753768844 10.804020100502512 11.306532663316581 11.809045226130653 12.311557788944722 12.814070351758794 13.316582914572862 13.819095477386934 14.321608040201003 14.824120603015075 15.326633165829143 15.829145728643216 16.331658291457284 16.834170854271353 17.336683417085425 17.839195979899497 18.341708542713565 18.844221105527634 19.346733668341706 19.849246231155778 20.351758793969847 20.854271356783915 21.356783919597987 21.859296482412059 22.361809045226128 22.864321608040196 23.366834170854268 23.86934673366834 24.371859296482409 24.874371859296478 25.37688442211055 25.879396984924622 26.38190954773869 26.884422110552759 27.386934673366831 27.889447236180903 28.391959798994971 28.89447236180904 29.396984924623112 29.899497487437184 30.402010050251253 30.904522613065321 31.407035175879393 31.909547738693465 32.412060301507537 32.914572864321606 33.417085427135675 33.91959798994975 34.422110552763819 34.924623115577887 35.427135678391963 35.929648241206031 36.4321608040201 36.934673366834168 37.437185929648237 37.939698492462313 38.442211055276381 38.94472361809045 39.447236180904525 39.949748743718594 40.452261306532662 40.954773869346731 41.457286432160799 41.959798994974875 42.462311557788944 42.964824120603012 43.467336683417088 43.969849246231156 44.472361809045225 44.974874371859293 45.477386934673362 45.979899497487438 46.482412060301506 46.984924623115575 47.48743718592965 47.989949748743719 48.492462311557787 48.994974874371856 49.497487437185924 50 50.502512562814069 51.005025125628137 51.507537688442213 52.010050251256281 52.51256281407035 53.015075376884418 53.517587939698487 54.020100502512562 54.522613065326631 55.0251256281407 55.527638190954775 56.030150753768844 56.532663316582912 57.035175879396981 57.537688442211049 58.040201005025125 58.542713567839193 59.045226130653262 59.547738693467338 60.050251256281406 60.552763819095475 61.055276381909543 61.557788944723612 62.060301507537687 62.562814070351756 63.065326633165824 63.5678391959799 64.070351758793961 64.572864321608037 65.075376884422113 65.577889447236174 66.08040201005025 66.582914572864311 67.085427135678387 67.587939698492463 68.090452261306524 68.5929648241206 69.095477386934675 69.597989949748737 70.100502512562812 70.603015075376888 71.105527638190949 71.608040201005025 72.110552763819086 72.613065326633162 73.115577889447238 73.618090452261299 74.120603015075375 74.623115577889436 75.125628140703512 75.628140703517587 76.130653266331649 76.633165829145725 77.1356783919598 77.638190954773862 78.140703517587937 78.643216080402013 79.145728643216074 79.64824120603015 80.150753768844211 80.653266331658287 81.155778894472363 81.658291457286424 82.1608040201005 82.663316582914561 83.165829145728637 83.668341708542712 84.170854271356774 84.673366834170849 85.175879396984925 85.678391959798986 86.180904522613062 86.683417085427138 87.185929648241199 87.688442211055275 88.190954773869336 88.693467336683412 89.19597989949 7488 89.698492462311549 90.201005025125625 90.703517587939686 91.206030150753762 91.708542713567837 92.211055276381899 92.713567839195974 93.21608040201005 93.718592964824111 94.221105527638187 94.723618090452263 95.226130653266324 95.7286432160804 96.231155778894461 96.733668341708537 97.236180904522612 97.738693467336674 98.241206030150749 98.743718592964811 99.246231155778887 99.748743718592962 1.1339999999999999 1.137 1.163 1.284 1.3120000000000001 1.3460000000000001 1.367 1.3720000000000001 1.389 1.397 1.415 1.4179999999999999 1.4279999999999999 1.43 1.45 1.4510000000000001 1.4570000000000001 1.458 1.476 1.4770000000000001 1.4790000000000001 1.4830000000000001 1.4950000000000001 1.5009999999999999 1.5009999999999999 1.504 1.506 1.5249999999999999 1.528 1.528 1.5289999999999999 1.536 1.54 1.546 1.5589999999999999 1.5620000000000001 1.575 1.587 1.59 1.6 1.63 1.6319999999999999 1.6679999999999999 1.671 1.6830000000000001 1.6910000000000001 1.702 1.7070000000000001 1.7350000000000001 1.75 1.7569999999999999 1.76 1.764 1.794 1.8 1.8120000000000001 1.8320000000000001 1.835 1.867 1.875 1.877 1.885 1.9 1.907 1.909 1.925 1.9390000000000001 1.948 1.9490000000000001 1.984 1.9870000000000001 1.988 1.9950000000000001 2 2 2.0219999999999998 2.0329999999999999 2.0430000000000001 2.0550000000000002 2.077 2.0910000000000002 2.097 2.0979999999999999 2.1349999999999998 2.1419999999999999 2.1459999999999999 2.1480000000000001 2.157 2.1709999999999998 2.1709999999999998 2.1720000000000002 2.1829999999999998 2.19 2.2040000000000002 2.2170000000000001 2.2269999999999999 2.2349999999999999 2.2509999999999999 2.258 2.262 2.2639999999999998 2.266 2.2789999999999999 2.2930000000000001 2.3159999999999998 2.34 2.383 2.391 2.3929999999999998 2.4089999999999998 2.41 2.41 2.4220000000000002 2.4300000000000002 2.4460000000000002 2.4809999999999999 2.4900000000000002 2.5 2.5308062840941101 2.5379999999999998 2.5430000000000001 2.5720000000000001 2.5870000000000002 2.6019999999999999 2.617 2.621 2.6360000000000001 2.6389999999999998 2.6789999999999998 2.7719999999999998 2.8580000000000001 2.8889999999999998 2.9089999999999998 2.996 3 3.05 3.0510000000000002 3.0550000000000002 3.109 3.1589999999999998 3.1619999999999999 3.1739999999999999 3.1949999999999998 3.2010000000000001 3.2290000000000001 3.3 3.3069999999999999 3.488 3.5 3.589 3.7 3.75 3.7629999999999999 3.7829999999999999 3.7989999999999999 3.84 3.8479999999999999 3.8639999999999999 3.988 4.0410000000000004 4.0510000000000002 4.2240000000000002 4.2249999999999996 4.2430000000000003 4.2699999999999996 4.2869999999999999 4.3609999999999998 4.3844662585282403 4.423 4.4420000000000002 4.4930000000000003 4.5350000000000001 4.6050000000000004 4.6230000000000002 4.6890000000000001 4.7130000000000001 4.7279999999999998 4.742 4.8769999999999998 4.9379999999999997 4.9800000000000004 5.032 5.0380000000000003 5.0780000000000003 5.1349999999999998 5.282 5.431 5.4850000000000003 5.4989999999999997 5.7370000000000001 5.75 5.9009999999999998 5.9180000000000001 5.968 5.968 6.117 6.2830000000000004 6.3 6.9249999999999998Sample Percentile
fertility
ln(Fertility)Onln(ppgdo)
| ppgdp | fertility | ln(ppgdp) | ln(ferility) | SUMMARY OUTPUT | ||||||||||||
| Afghanistan | 499 | 5.968 | 6.2126060958 | 1.7864118629 | ||||||||||||
| Albania | 3677.2 | 1.525 | 8.209906872 | 0.4219944101 | Regression Statistics | |||||||||||
| Algeria | 4473 | 2.142 | 8.4058146034 | 0.761739972 | Multiple R | 0.7252482571 | ||||||||||
| Angola | 4321.9 | 5.135 | 8.3714503994 | 1.6360798434 | R Square | 0.5259850345 | ||||||||||
| Anguilla | 13750.1 | 2 | 9.5288013758 | 0.6931471806 | Adjusted R Square | 0.5235788671 | ||||||||||
| Argentina | 9162.1 | 2.172 | 9.122830689 | 0.7756484021 | Standard Error | 0.3071114681 | ||||||||||
| Armenia | 3030.7 | 1.735 | 8.0165488949 | 0.5510074134 | Observations | 199 | ||||||||||
| Aruba | 22851.5 | 1.671 | 10.0367720397 | 0.5134222496 | ||||||||||||
| Australia | 57118.9 | 1.949 | 10.9528903391 | 0.6673164205 | ANOVA | |||||||||||
| Austria | 45158.8 | 1.346 | 10.7179404457 | 0.2971372312 | df | SS | MS | F | Significance F | |||||||
| Azerbaijan | 5637.6 | 2.148 | 8.637213722 | 0.7645371766 | Regression | 1 | 20.6176721099 | 20.6176721099 | 218.5986927254 | 9.06235683202192E-34 | ||||||
| Bahamas | 22461.6 | 1.877 | 10.0195624635 | 0.6296747576 | Residual | 197 | 18.5805384058 | 0.0943174538 | ||||||||
| Bahrain | 18184.1 | 2.43 | 9.8083028649 | 0.8878912574 | Total | 198 | 39.1982105157 | |||||||||
| Bangladesh | 670.4 | 2.157 | 6.5078745492 | 0.7687183674 | ||||||||||||
| Barbados | 14497.3 | 1.575 | 9.5817177042 | 0.4542552723 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||||
| Belarus | 5702 | 1.479 | 8.6485722695 | 0.3913661837 | Intercept | 2.6655073378 | 0.1205657647 | 22.1083268954 | 2.93530254356805E-55 | 2.4277421211 | 2.9032725545 | 2.4277421211 | 2.9032725545 | |||
| Belgium | 43814.8 | 1.835 | 10.6877269388 | 0.6070444815 | ln(ppgdp) | -0.2071497864 | 0.0140107282 | -14.7850834534 | 9.06235683202192E-34 | -0.2347800498 | -0.1795195229 | -0.2347800498 | -0.1795195229 | |||
| Belize | 4495.8 | 2.679 | 8.4108989066 | 0.9854435906 | ||||||||||||
| Benin | 741.1 | 5.078 | 6.608135569 | 1.6249174833 | ||||||||||||
| Bermuda | 92624.7 | 1.76 | 11.4363111237 | 0.5653138091 | ||||||||||||
| Bhutan | 2047.2 | 2.258 | 7.6242282848 | 0.8144794657 | RESIDUAL OUTPUT | |||||||||||
| Bolivia | 1977.9 | 3.229 | 7.5897909548 | 1.1721724918 | ||||||||||||
| Bosnia and Herzegovina | 4477.7 | 1.134 | 8.4068648007 | 0.1257512053 | Row | Observation | Predicted ln(ferility) | Residuals | ||||||||
| Botswana | 7402.9 | 2.617 | 8.9096270943 | 0.9620286235 | 2 | 1 | Afghanistan | 1.3785673124 | 0.4078445505 | Max | 0.9559557215 | |||||
| Brazil | 10715.6 | 1.8 | 9.2794559026 | 0.5877866649 | 3 | 2 | Albania | 0.9648268833 | -0.5428324732 | Min | -0.7982758851 | |||||
| Brunei Darussalam | 32647.6 | 1.984 | 10.3935266251 | 0.6851150089 | 4 | 3 | Algeria | 0.9242446386 | -0.1625046665 | |||||||
| Bulgaria | 6365.1 | 1.546 | 8.7585852218 | 0.4356709502 | 5 | 4 | Angola | 0.9313631761 | 0.7047166673 | |||||||
| Burkina Faso | 519.7 | 5.75 | 6.253251722 | 1.7491998548 | 6 | 5 | Anguilla | 0.6916181686 | 0.001529012 | |||||||
| Burundi | 176.6 | 4.051 | 5.1738872882 | 1.3989637642 | 7 | 6 | Argentina | 0.7757149096 | -0.0000665075 | |||||||
| Cambodia | 797.2 | 2.422 | 6.6811055883 | 0.8845936451 | 8 | 7 | Armenia | 1.0048809469 | -0.4538735335 | |||||||
| Cameroon | 1206.6 | 4.287 | 7.095561766 | 1.4555871876 | 9 | 8 | Aruba | 0.5863921541 | -0.0729699045 | |||||||
| Canada | 46360.9 | 1.691 | 10.7442117106 | 0.5253200699 | 10 | 9 | Australia | 0.3966184441 | 0.2706979764 | |||||||
| Cape Verde | 3244 | 2.279 | 8.0845624152 | 0.8237367503 | 11 | 10 | Austria | 0.4452882643 | -0.1481510331 | |||||||
| Cayman Islands | 57047.9 | 1.6 | 10.9516465448 | 0.4700036292 | 12 | 11 | Azerbaijan | 0.8763103606 | -0.1117731839 | |||||||
| Central African Republic | 450.8 | 4.423 | 6.1110237822 | 1.4868181989 | 13 | 12 | Bahamas | 0.5899571141 | 0.0397176435 | |||||||
| Chad | 727.4 | 5.737 | 6.5894765326 | 1.7469364256 | 14 | 13 | Bahrain | 0.6337194948 | 0.2541717625 | |||||||
| Chile | 11887.7 | 1.832 | 9.3832595311 | 0.6054082663 | 15 | 14 | Bangladesh | 1.3174025153 | -0.5486841479 | |||||||
| China | 4354 | 1.559 | 8.3788502418 | 0.4440445901 | 16 | 15 | Barbados | 0.6806565625 | -0.2264012902 | |||||||
| Colombia | 6222.8 | 2.293 | 8.7359752452 | 0.8298610039 | 17 | 16 | Belarus | 0.8739574399 | -0.4825912562 | |||||||
| Comoros | 736.6 | 4.742 | 6.602045004 | 1.5564589876 | 18 | 17 | Belgium | 0.4515469858 | 0.1554974957 | |||||||
| Congo | 2665.1 | 4.442 | 7.8879968593 | 1.4911047255 | 19 | 18 | Belize | 0.9231914263 | 0.0622521643 | |||||||
| Cook Islands | 12212.1 | 2.5308062841 | 9.4101825425 | 0.9285379413 | 20 | 19 | Benin | 1.2966334665 | 0.3282840168 | |||||||
| Costa Rica | 7703.8 | 1.812 | 8.9494689926 | 0.5944312076 | 21 | 20 | Bermuda | 0.2964779318 | 0.2688358772 | |||||||
| Cote dIvoire | 1154.1 | 4.224 | 7.0510760984 | 1.4407825464 | 22 | 21 | Bhutan | 1.0861500775 | -0.2716706118 | |||||||
| Croatia | 13819.5 | 1.501 | 9.5338359172 | 0.4061315527 | 23 | 22 | Bolivia | 1.093283763 | 0.0788887287 | |||||||
| Cuba | 5704.4 | 1.451 | 8.6489930859 | 0.3722529739 | 24 | 23 | Bosnia and Herzegovina | 0.9240270904 | -0.7982758851 | |||||||
| Cyprus | 28364.3 | 1.458 | 10.2528865912 | 0.3770656336 | 25 | 24 | Botswana | 0.8198799887 | 0.1421486348 | |||||||
| Czech Republic | 18838.8 | 1.501 | 9.8436738518 | 0.4061315527 | 26 | 25 | Brazil | 0.7432700301 | -0.1554833652 | |||||||
| Democratic Republic of the Congo | 200.6 | 5.485 | 5.3013128755 | 1.7020170937 | 27 | 26 | Brunei Darussalam | 0.5124905179 | 0.1726244909 | |||||||
| Denmark | 55830.2 | 1.885 | 10.9300702206 | 0.6339278209 | 28 | 27 | Bulgaria | 0.8511682803 | -0.4154973302 | |||||||
| Djibouti | 1282.6 | 3.589 | 7.1566445467 | 1.2778736122 | 29 | 28 | Burkina Faso | 1.3701475796 | 0.3790522752 | |||||||
| Dominica | 7020.8 | 3 | 8.8566324506 | 1.0986122887 | 30 | 29 | Burundi | 1.5937376915 | -0.1947739272 | |||||||
| Dominican Republic | 5195.4 | 2.49 | 8.5555288977 | 0.9122827105 | 31 | 30 | Cambodia | 1.2815177426 | -0.3969240974 | |||||||
| East Timor | 706.1 | 5.918 | 6.5597568705 | 1.777998554 | 32 | 31 | Cameroon | 1.1956632339 | 0.2599239537 | |||||||
| Ecuador | 4072.6 | 2.393 | 8.3120368951 | 0.8725478089 | 33 | 32 | Canada | 0.4398461774 | 0.0854738925 | |||||||
| Egypt | 2653.7 | 2.636 | 7.8837101716 | 0.9692626166 | 34 | 33 | Cape Verde | 0.9907919607 | -0.1670552105 | |||||||
| El Salvador | 3425.6 | 2.171 | 8.1390319178 | 0.7751878909 | 35 | 34 | Cayman Islands | 0.3968760958 | 0.0731275334 | |||||||
| Equatorial Guinea | 16852.4 | 4.98 | 9.7322483589 | 1.605429891 | 36 | 35 | Central African Republic | 1.3996100669 | 0.087208132 | |||||||
| Eritrea | 429.1 | 4.243 | 6.061689992 | 1.4452705662 | 37 | 36 | Chad | 1.3004986819 | 0.4464377437 | |||||||
| Estonia | 14135.4 | 1.702 | 9.5564375683 | 0.5318040302 | 38 | 37 | Chile | 0.7217671306 | -0.1163588644 | |||||||
| Ethiopia | 324.6 | 3.848 | 5.7825936551 | 1.3475535328 | 39 | 38 | China | 0.9298303003 | -0.4857857102 | |||||||
| Fiji | 3545.7 | 2.602 | 8.1734908807 | 0.9562803801 | 40 | 39 | Colombia | 0.8558519322 | -0.0259909283 | |||||||
| Finland | 44501.7 | 1.875 | 10.7032826697 | 0.6286086594 | 41 | 40 | Comoros | 1.2978951257 | 0.2585638619 | |||||||
| France | 39545.9 | 1.987 | 10.5852173016 | 0.6866259636 | 42 | 41 | Congo | 1.0315104736 | 0.4595942518 | |||||||
| French Polynesia | 24669 | 2.033 | 10.1133026736 | 0.7095125346 | 43 | 42 | Cook Islands | 0.7161900346 | 0.2123479068 | |||||||
| Gabon | 12468.8 | 3.195 | 9.4309848031 | 1.1615870878 | 44 | 43 | Costa Rica | 0.811626748 | -0.2171955404 | |||||||
| Gambia | 579.1 | 4.689 | 6.3614751742 | 1.5452193401 | 45 | 44 | Cote dIvoire | 1.2048784305 | 0.235904116 | |||||||
| Georgia | 2680.3 | 1.528 | 7.8936840075 | 0.4239596907 | 46 | 45 | Croatia | 0.6905752644 | -0.2844437118 | |||||||
| Germany | 39857.1 | 1.457 | 10.5930558365 | 0.3763795272 | 47 | 46 | Cuba | 0.8738702679 | -0.501617294 | |||||||
| Ghana | 1333.2 | 3.988 | 7.1953373464 | 1.3832898521 | 48 | 47 | Cyprus | 0.5416240709 | -0.1645584373 | |||||||
| Greece | 26503.8 | 1.54 | 10.1850433979 | 0.4317824164 | 49 | 48 | Czech Republic | 0.6263924024 | -0.2202608498 | |||||||
| Greenland | 35292.7 | 2.217 | 10.4714314227 | 0.7961549306 | 50 | 49 | Democratic Republic of the Congo | 1.5673415083 | 0.1346755855 | |||||||
| Grenada | 7429 | 2.171 | 8.9131465392 | 0.7751878909 | 51 | 50 | Denmark | 0.4013456268 | 0.2325821941 | |||||||
| Guatemala | 2882.3 | 3.84 | 7.9663438655 | 1.3454723666 | 52 | 51 | Djibouti | 1.1830099489 | 0.0948636632 | |||||||
| Guinea | 427.5 | 5.032 | 6.0579542884 | 1.6158175194 | 53 | 52 | Dominica | 0.8308578178 | 0.2677544708 | |||||||
| Guinea-Bissau | 539.4 | 4.877 | 6.2904574107 | 1.5845302767 | 54 | 53 | Dominican Republic | 0.8932313545 | 0.019051356 | |||||||
| Guyana | 2996 | 2.19 | 8.0050333446 | 0.7839015438 | 55 | 54 | East Timor | 1.3066551035 | 0.4713434504 | |||||||
| Haiti | 612.7 | 3.159 | 6.4178754197 | 1.1502555218 | 56 | 55 | Ecuador | 0.9436706708 | -0.0711228619 | |||||||
| Honduras | 2026.2 | 2.996 | 7.6139173966 | 1.0972780657 | 57 | 56 | Egypt | 1.0323984601 | -0.0631358434 | |||||||
| Hong Kong | 31823.7 | 1.137 | 10.3679665742 | 0.1283932148 | 58 | 57 | El Salvador | 0.9795086149 | -0.204320724 | |||||||
| Hungary | 12884 | 1.43 | 9.4637415105 | 0.3576744443 | 59 | 58 | Equatorial Guinea | 0.6494741695 | 0.9559557215 | |||||||
| Iceland | 39278 | 2.098 | 10.5784198447 | 0.74098451 | 60 | 59 | Eritrea | 1.409829551 | 0.0354410152 | |||||||
| India | 1406.4 | 2.538 | 7.2487885269 | 0.9313763693 | 61 | 60 | Estonia | 0.6858933372 | -0.1540893071 | |||||||
| Indonesia | 2949.3 | 2.055 | 7.989323133 | 0.7202758479 | 62 | 61 | Ethiopia | 1.4676442976 | -0.1200907648 | |||||||
| Iran | 5227.1 | 1.587 | 8.56161191 | 0.4618454415 | 63 | 62 | Fiji | 0.9723704481 | -0.016090068 | |||||||
| Iraq | 888.5 | 4.535 | 6.7895346476 | 1.5118250836 | 64 | 63 | Finland | 0.4483246195 | 0.1802840399 | |||||||
| Ireland | 46220.3 | 2.097 | 10.7411743745 | 0.7405077519 | 65 | 64 | France | 0.4727818353 | 0.2138441283 | |||||||
| Israel | 29311.6 | 2.909 | 10.2857386211 | 1.0678093795 | 66 | 65 | French Polynesia | 0.5705388496 | 0.138973685 | |||||||
| Italy | 33877.1 | 1.476 | 10.4304945489 | 0.3893357262 | 67 | 66 | Gabon | 0.7118808507 | 0.4497062371 | |||||||
| Jamaica | 4899 | 2.262 | 8.4967863816 | 0.8162493777 | 68 | 67 | Gambia | 1.3477291146 | 0.1974902255 | |||||||
| Japan | 43140.9 | 1.418 | 10.672226782 | 0.3492474281 | 69 | 68 | Georgia | 1.0303323821 | -0.6063726914 | |||||||
| Jordan | 4445.3 | 2.889 | 8.3996026372 | 1.0609104215 | 70 | 69 | Germany | 0.4711580844 | -0.0947785572 | |||||||
| Kazakhstan | 9166.7 | 2.481 | 9.1233326313 | 0.9086617047 | 71 | 70 | Ghana | 1.1749947437 | 0.2082951084 | |||||||
| Kenya | 801.8 | 4.623 | 6.6868592002 | 1.531043845 | 72 | 71 | Greece | 0.5556777739 | -0.1238953575 | |||||||
| Kiribati | 1468.2 | 3.5 | 7.2917924397 | 1.2527629685 | 73 | 72 | Greenland | 0.4963525558 | 0.2998023749 | |||||||
| Kuwait | 45430.4 | 2.251 | 10.7239367635 | 0.8113745619 | 74 | 73 | Grenada | 0.8191509365 | -0.0439630456 | |||||||
| Kyrgyzstan | 865.4 | 2.621 | 6.7631918278 | 0.9635559243 | 75 | 74 | Guatemala | 1.015280908 | 0.3301914586 | |||||||
| Laos | 1047.6 | 2.543 | 6.9542571126 | 0.9333444864 | 76 | 75 | Guinea | 1.4106034012 | 0.2052141182 | |||||||
| Latvia | 10663 | 1.506 | 9.274535084 | 0.4094571294 | 77 | 76 | Guinea-Bissau | 1.3624404291 | 0.2220898476 | |||||||
| Lebanon | 9283.7 | 1.764 | 9.1360154532 | 0.5675839576 | 78 | 77 | Guyana | 1.0072663907 | -0.2233648469 | |||||||
| Lesotho | 980.7 | 3.051 | 6.8882666024 | 1.1154694057 | 79 | 78 | Haiti | 1.3360458158 | -0.1857902939 | |||||||
| Liberia | 218.6 | 5.038 | 5.3872435757 | 1.6170091779 | 80 | 79 | Honduras | 1.0882859758 | 0.0089920899 | |||||||
| Libya | 11320.8 | 2.41 | 9.3343970206 | 0.8796267475 | 81 | 80 | Hong Kong | 0.517785277 | -0.3893920623 | |||||||
| Lithuania | 10975.5 | 1.495 | 9.303420795 | 0.4021262068 | 82 | 81 | Hungary | 0.7050953058 | -0.3474208615 | |||||||
| Luxembourg | 105095.4 | 1.683 | 11.5626237881 | 0.5205779152 | 83 | 82 | Iceland | 0.474189927 | 0.266794583 | |||||||
| Macao | 49990.2 | 1.163 | 10.8195822652 | 0.1510028735 | 84 | 83 | India | 1.1639223431 | -0.2325459738 | |||||||
| Madagascar | 421.9 | 4.493 | 6.0447683191 | 1.5025206301 | 85 | 84 | Indonesia | 1.0105207577 | -0.2902449097 | |||||||
| Malawi | 357.4 | 5.968 | 5.8788556027 | 1.7864118629 | 86 | 85 | Iran | 0.8919712598 | -0.4301258183 | |||||||
| Malaysia | 8372.8 | 2.572 | 9.0327436356 | 0.9446838064 | 87 | 86 | Iraq | 1.2590566861 | 0.2527683975 | |||||||
| Maldives | 4684.5 | 1.668 | 8.4520144654 | 0.5116253039 | 88 | 87 | Ireland | 0.4404753609 | 0.300032391 | |||||||
| Mali | 598.8 | 6.117 | 6.3949276525 | 1.8110717803 | 89 | 88 | Israel | 0.5348187799 | 0.5329905996 | |||||||
| Malta | 19599.2 | 1.284 | 9.8832440281 | 0.2499802053 | 90 | 89 | Italy | 0.5048326204 | -0.1154968942 | |||||||
| Marshall Islands | 3069.4 | 4.3844662585 | 8.0292373817 | 1.4780678986 | 91 | 90 | Jamaica | 0.9053998541 | -0.0891504765 | |||||||
| Mauritania | 1131.1 | 4.361 | 7.0309458895 | 1.4727013889 | 92 | 91 | Japan | 0.45475784 | -0.1055104119 | |||||||
| Mauritius | 7488.3 | 1.59 | 8.9210970815 | 0.4637340162 | 93 | 92 | Jordan | 0.925531446 | 0.1353789754 | |||||||
| Mexico | 9100.7 | 2.227 | 9.1161066126 | 0.8006553883 | 94 | 93 | Kazakhstan | 0.7756109324 | 0.1330507723 | |||||||
| Micronesia | 2678.2 | 3.307 | 7.8929002061 | 1.196041434 | 95 | 94 | Kenya | 1.2803258831 | 0.2507179619 | |||||||
| Moldova | 1625.8 | 1.45 | 7.3937552813 | 0.3715635564 | 96 | 95 | Kiribati | 1.1550140918 | 0.0977488767 | |||||||
| Mongolia | 2246.7 | 2.446 | 7.7172177519 | 0.8944540373 | 97 | 96 | Kuwait | 0.4440461284 | 0.3673284336 | |||||||
| Montenegro | 6509.8 | 1.63 | 8.7810640128 | 0.4885800148 | 98 | 97 | Kyrgyzstan | 1.2645135956 | -0.3009576713 | |||||||
| Morocco | 2865 | 2.183 | 7.9603236291 | 0.7807000776 | 99 | 98 | Laos | 1.2249344627 | -0.2915899762 | |||||||
| Mozambique | 407.5 | 4.713 | 6.0100409327 | 1.5503246479 | 100 | 99 | Latvia | 0.7442893766 | -0.3348322472 | |||||||
| Myanmar | 876.2 | 1.939 | 6.7755943754 | 0.6621723763 | 101 | 100 | Lebanon | 0.7729836885 | -0.205399731 | |||||||
| Namibia | 5124.7 | 3.055 | 8.5418272657 | 1.1167795926 | 102 | 101 | Lesotho | 1.2386043828 | -0.123134977 | |||||||
| Nauru | 6190.1 | 3.3 | 8.7307065206 | 1.1939224685 | 103 | 102 | Liberia | 1.5495409821 | 0.0674681959 | |||||||
| Nepal | 534.7 | 2.587 | 6.281705842 | 0.9504989032 | 104 | 103 | Libya | 0.7318889892 | 0.1477377583 | |||||||
| Neth Antilles | 20321.1 | 1.9 | 9.9194150341 | 0.6418538862 | 105 | 104 | Lithuania | 0.7383057078 | -0.3361795009 | |||||||
| Netherlands | 46909.7 | 1.794 | 10.7559797561 | 0.5844477636 | 106 | 105 | Luxembourg | 0.2703122904 | 0.2502656248 | |||||||
| New Caledonia | 35319.5 | 2.091 | 10.4721904983 | 0.7376424204 | 107 | 106 | Macao | 0.4242331831 | -0.2732303096 | |||||||
| New Zealand | 32372.1 | 2.135 | 10.3850522197 | 0.7584666467 | 108 | 107 | Madagascar | 1.4133348719 | 0.0891857581 | |||||||
| Nicaragua | 1131.9 | 2.5 | 7.0316529156 | 0.9162907319 | 109 | 108 | Malawi | 1.4477036557 | 0.3387082072 | |||||||
| Niger | 357.7 | 6.925 | 5.8796946463 | 1.9351380521 | 110 | 109 | Malaysia | 0.7943764235 | 0.1503073829 | |||||||
| Nigeria | 1239.8 | 5.431 | 7.1227053553 | 1.6921232791 | 111 | 110 | Maldives | 0.914674347 | -0.4030490431 | |||||||
| North Korea | 504 | 1.988 | 6.2225762681 | 0.6871291082 | 112 | 111 | Mali | 1.3407994408 | 0.4702723394 | |||||||
| Norway | 84588.7 | 1.948 | 11.3455559669 | 0.6668032052 | 113 | 112 | Malta | 0.6181954489 | -0.3682152436 | |||||||
| Oman | 20791 | 2.146 | 9.9422754797 | 0.7636056442 | 114 | 113 | Marshall Islands | 1.0022525296 | 0.475815369 | |||||||
| Pakistan | 1003.2 | 3.201 | 6.9109501699 | 1.163463261 | 115 | 114 | Mauritania | 1.2090483989 | 0.2636529899 | |||||||
| Palau | 10821.8 | 2 | 9.2893178972 | 0.6931471806 | 116 | 115 | Mauritius | 0.8175039833 | -0.3537699671 | |||||||
| Palestinian Territory | 1819.5 | 4.27 | 7.5063170171 | 1.4516138272 | 117 | 116 | Mexico | 0.7771078006 | 0.0235475877 | |||||||
| Panama | 7614 | 2.409 | 8.9377439369 | 0.8792117236 | 118 | 117 | Micronesia | 1.0304947464 | 0.1655466876 | |||||||
| Papua New Guinea | 1428.4 | 3.799 | 7.2643102157 | 1.3347378742 | 119 | 118 | Moldova | 1.1338925109 | -0.7623289545 | |||||||
| Paraguay | 2771.1 | 2.858 | 7.9269996323 | 1.0501220795 | 120 | 119 | Mongolia | 1.0668873292 | -0.172433292 | |||||||
| Peru | 5410.7 | 2.41 | 8.5961337535 | 0.8796267475 | 121 | 120 | Montenegro | 0.8465118036 | -0.3579317888 | |||||||
| Philippines | 2140.1 | 3.05 | 7.6686078359 | 1.1151415906 | 122 | 121 | Morocco | 1.0165279987 | -0.2358279211 | |||||||
| Poland | 12263.2 | 1.415 | 9.4143581869 | 0.3471295311 | 123 | 122 | Mozambique | 1.4205286426 | 0.1297960053 | |||||||
| Portugal | 21437.6 | 1.312 | 9.9729016686 | 0.2715526905 | 124 | 123 | Myanmar | 1.2619444105 | -0.5997720343 | |||||||
| Puerto Rico | 26461 | 1.757 | 10.1834272298 | 0.5636078092 | 125 | 124 | Namibia | 0.8960696446 | 0.220709948 | |||||||
| Qatar | 72397.9 | 2.204 | 11.1899325724 | 0.7902738913 | 126 | 125 | Nauru | 0.8569433473 | 0.3369791211 | |||||||
| Republic of Korea | 21052.2 | 1.389 | 9.9547603467 | 0.3285840638 | 127 | 126 | Nepal | 1.3642533147 | -0.4137544115 | |||||||
| Romania | 7522.4 | 1.428 | 8.925640515 | 0.3562748639 | 128 | 127 | Neth Antilles | 0.6107026327 | 0.0311512534 | |||||||
| Russian Federation | 10351.4 | 1.529 | 9.2448770552 | 0.4246139269 | 129 | 128 | Netherlands | 0.4374084293 | 0.1470393343 | |||||||
| Rwanda | 532.3 | 5.282 | 6.2772072402 | 1.6643048139 | 130 | 129 | New Caledonia | 0.4961953134 | 0.241447107 | |||||||
| Saint Lucia | 6677.1 | 1.907 | 8.8064390405 | 0.6455313266 | 131 | 130 | New Zealand | 0.5142459892 | 0.2442206575 | |||||||
| Samoa | 3343.3 | 3.763 | 8.1147136221 | 1.3252165116 | 132 | 131 | Nicaragua | 1.2089019386 | -0.2926112067 | |||||||
| Sao Tome and Principe | 1283.3 | 3.488 | 7.1571901643 | 1.249328506 | 133 | 132 | Niger | 1.447529848 | 0.4876082041 | |||||||
| Saudi Arabia | 15835.9 | 2.639 | 9.6700347935 | 0.9704000575 | 134 | 133 | Nigeria | 1.1900404452 | 0.5020828339 | |||||||
| Senegal | 1032.7 | 4.605 | 6.9399320107 | 1.5271426697 | 135 | 134 | North Korea | 1.3765019933 | -0.6893728851 | |||||||
| Serbia | 5123.2 | 1.562 | 8.5415345228 | 0.4459670514 | 136 | 135 | Norway | 0.3152778432 | 0.351525362 | |||||||
| Seychelles | 11450.6 | 2.34 | 9.3457974094 | 0.8501509294 | 137 | 136 | Oman | 0.6059670963 | 0.1576385479 | |||||||
| Sierra Leone | 351.7 | 4.728 | 5.8627785395 | 1.5535022801 | 138 | 137 | Pakistan | 1.2339054866 | -0.0704422256 | |||||||
| Singapore | 43783.1 | 1.367 | 10.6870031772 | 0.3126185577 | 139 | 138 | Palau | 0.74122712 | -0.0480799395 | |||||||
| Slovakia | 15976 | 1.372 | 9.6788428751 | 0.3162695293 | 140 | 139 | Palestinian Territory | 1.1105753714 | 0.3410384558 | |||||||
| Slovenia | 23109.8 | 1.477 | 10.048012049 | 0.3900130035 | 141 | 140 | Panama | 0.8140555908 | 0.0651561329 | |||||||
| Solomon Islands | 1193.5 | 4.041 | 7.0846454458 | 1.3964921861 | 142 | 141 | Papua New Guinea | 1.1607070286 | 0.1740308456 | |||||||
| Somalia | 114.8 | 6.283 | 4.7431914839 | 1.8378475734 | 143 | 142 | Paraguay | 1.0234310576 | 0.026691022 | |||||||
| South Africa | 7254.8 | 2.383 | 8.8894185977 | 0.8683601981 | 144 | 143 | Peru | 0.8848200673 | -0.0051933198 | |||||||
| Spain | 30542.8 | 1.504 | 10.3268842576 | 0.4081282255 | 145 | 144 | Philippines | 1.076956863 | 0.0381847277 | |||||||
| Sri Lanka | 2375.3 | 2.235 | 7.7728790243 | 0.8042412281 | 146 | 145 | Poland | 0.7153250507 | -0.3681955196 | |||||||
| St Vincent and Grenadines | 6171.7 | 1.995 | 8.7277296057 | 0.6906440503 | 147 | 146 | Portugal | 0.5996228878 | -0.3280701973 | |||||||
| Sudan | 1824.9 | 4.225 | 7.50928047 | 1.4410192608 | 148 | 147 | Puerto Rico | 0.5560125628 | 0.0075952464 | |||||||
| Suriname | 7018 | 2.266 | 8.8562335561 | 0.8180161626 | 149 | 148 | Qatar | 0.3475151961 | 0.4427586952 | |||||||
| Swaziland | 3311.2 | 3.174 | 8.1050659404 | 1.1549926221 | 150 | 149 | Republic of Korea | 0.6033808588 | -0.274796795 | |||||||
| Sweden | 48906.2 | 1.925 | 10.7976594568 | 0.6549259677 | 151 | 150 | Romania | 0.8165628121 | -0.4602879481 | |||||||
| Switzerland | 68880.2 | 1.536 | 11.1401240427 | 0.4291816347 | 152 | 151 | Russian Federation | 0.7504330309 | -0.325819104 | |||||||
| Syria | 2931.5 | 2.772 | 7.9832695164 | 1.0195690813 | 153 | 152 | Rwanda | 1.3651851991 | 0.2991196148 | |||||||
| Tajikistan | 816 | 3.162 | 6.704414355 | 1.1512047388 | 154 | 153 | Saint Lucia | 0.841255372 | -0.1957240454 | |||||||
| Tanzania | 516 | 5.499 | 6.2461067655 | 1.7045662575 | 155 | 154 | Samoa | 0.9845461447 | 0.340670367 | |||||||
| TFYR Macedonia | 4434.5 | 1.397 | 8.3971701488 | 0.3343270803 | 156 | 155 | Sao Tome and Principe | 1.1828969244 | 0.0664315817 | |||||||
| Thailand | 4612.8 | 1.528 | 8.4365903269 | 0.4239596907 | 157 | 156 | Saudi Arabia | 0.6623616963 | 0.3080383612 | |||||||
| Togo | 524.6 | 3.864 | 6.2626360674 | 1.3517029164 | 158 | 157 | Senegal | 1.2279019045 | 0.2992407652 | |||||||
| Tonga | 3543.1 | 3.783 | 8.1727573291 | 1.3305173457 | 159 | 158 | Serbia | 0.8961302863 | -0.4501632348 | |||||||
| Trinidad and Tobago | 15205.1 | 1.632 | 9.6293861769 | 0.4898062565 | 160 | 159 | Seychelles | 0.7295274011 | 0.1206235282 | |||||||
| Tunisia | 4222.1 | 1.909 | 8.3480879136 | 0.6465795447 | 161 | 160 | Sierra Leone | 1.4510340159 | 0.1024682642 | |||||||
| Turkey | 10095.1 | 2.022 | 9.2198054366 | 0.7040871206 | 162 | 161 | Singapore | 0.4516969129 | -0.1390783551 | |||||||
| Turkmenistan | 4587.5 | 2.316 | 8.4310904924 | 0.8398415597 | 163 | 162 | Slovakia | 0.6605371041 | -0.3442675748 | |||||||
| Tuvalu | 3187.2 | 3.7 | 8.0668980674 | 1.3083328197 | 164 | 163 | Slovenia | 0.5840637886 | -0.194050785 | |||||||
| Uganda | 509 | 5.901 | 6.2324480166 | 1.7751218281 | 165 | 164 | Solomon Islands | 1.1979245473 | 0.1985676388 | |||||||
| Ukraine | 3035 | 1.483 | 8.0179667035 | 0.3940670632 | 166 | 165 | Somalia | 1.6829562353 | 0.1548913381 | |||||||
| United Arab Emirates | 39624.7 | 1.707 | 10.5872079402 | 0.5347374438 | 167 | 166 | South Africa | 0.8240661745 | 0.0442940237 | |||||||
| United Kingdom | 36326.8 | 1.867 | 10.5003110399 | 0.6243328646 | 168 | 167 | Spain | 0.5262954701 | -0.1181672446 | |||||||
| United States | 46545.9 | 2.077 | 10.7481942015 | 0.7309245449 | 169 | 168 | Sri Lanka | 1.0553571086 | -0.2511158805 | |||||||
| Uruguay | 11952.4 | 2.043 | 9.388687374 | 0.7144193158 | 170 | 169 | St Vincent and Grenadines | 0.8575600146 | -0.1669159643 | |||||||
| Uzbekistan | 1427.3 | 2.264 | 7.2635398266 | 0.8171331603 | 171 | 170 | Sudan | 1.1099614928 | 0.331057768 | |||||||
| Vanuatu | 2963.5 | 3.75 | 7.9941262812 | 1.32175584 | 172 | 171 | Suriname | 0.8309404487 | -0.0129242861 | |||||||
| Venezuela | 13502.7 | 2.391 | 9.5106449444 | 0.8717116885 | 173 | 172 | Swaziland | 0.9865446599 | 0.1684479622 | |||||||
| Viet Nam | 1182.7 | 1.75 | 7.0755552393 | 0.5596157879 | 174 | 173 | Sweden | 0.4287744882 | 0.2261514795 | |||||||
| Yemen | 1437.2 | 4.938 | 7.2704520552 | 1.5969603909 | 175 | 174 | Switzerland | 0.3578330224 | 0.0713486123 | |||||||
| Zambia | 1237.8 | 6.3 | 7.1210908893 | 1.8405496334 | 176 | 175 | Syria | 1.0117747631 | 0.0077943183 | |||||||
| Zimbabwe | 573.1 | 3.109 | 6.3510602216 | 1.1343011311 | 177 | 176 | Tajikistan | 1.2766893365 | -0.1254845978 | |||||||
| 178 | 177 | Tanzania | 1.3716276558 | 0.3329386017 | ||||||||||||
| 179 | 178 | TFYR Macedonia | 0.9260353355 | -0.5917082552 | ||||||||||||
| 180 | 179 | Thailand | 0.917869454 | -0.4939097633 | ||||||||||||
| 181 | 180 | Togo | 1.3682036144 | -0.0165006981 | ||||||||||||
| 182 | 181 | Tonga | 0.9725224031 | 0.3579949425 | ||||||||||||
| 183 | 182 | Trinidad and Tobago | 0.6707820485 | -0.180975792 | ||||||||||||
| 184 | 183 | Tunisia | 0.93620271 | -0.2896231653 | ||||||||||||
| 185 | 184 | Turkey | 0.7556266114 | -0.0515394908 | ||||||||||||
| 186 | 185 | Turkmenistan | 0.9190087436 | -0.0791671839 | ||||||||||||
| 187 | 186 | Tuvalu | 0.9944511266 | 0.313881693 | ||||||||||||
| 188 | 187 | Uganda | 1.3744570627 | 0.4006647654 | ||||||||||||
| 189 | 188 | Ukraine | 1.0045872482 | -0.610520185 | ||||||||||||
| 190 | 189 | United Arab Emirates | 0.4723694749 | 0.0623679689 | ||||||||||||
| 191 | 190 | United Kingdom | 0.4903701492 | 0.1339627153 | ||||||||||||
| 192 | 191 | United States | 0.4390212053 | 0.2919033396 | ||||||||||||
| 193 | 192 | Uruguay | 0.7206427541 | -0.0062234383 | ||||||||||||
| 194 | 193 | Uzbekistan | 1.1608666145 | -0.3437334542 | ||||||||||||
| 195 | 194 | Vanuatu | 1.0095257866 | 0.3122300534 | ||||||||||||
| 196 | 195 | Venezuela | 0.6953792695 | 0.176332419 | ||||||||||||
| 197 | 196 | Viet Nam | 1.1998075817 | -0.6401917937 | ||||||||||||
| 198 | 197 | Yemen | 1.1594347479 | 0.4375256431 | ||||||||||||
| 199 | 198 | Zambia | 1.1903748815 | 0.6501747519 | ||||||||||||
| 200 | 199 | Zimbabwe | 1.3498865698 | -0.2155854387 |
MLR_Output
| XLMiner : Multiple Linear Regression | Date: 21-Sep-2016 03:55:09 | |||||||||||||||
| Output Navigator | Elapsed Times in Milliseconds | |||||||||||||||
| Inputs | Predictors | Regress. Model | ANOVA | Train. Score - Summary | Data read time | MLR Time | Report Time | Total | ||||||||
| Residuals-Fitted Values | Training Lift Chart | Train. Score - Detailed Rep. | 6 | 31 | 38 | 75 | ||||||||||
| Inputs | ||||||||||||||||
| Data | ||||||||||||||||
| Workbook | UN11.xlsx | |||||||||||||||
| Worksheet | Sheet1 | |||||||||||||||
| Data Range | $A$1:$B$200 | |||||||||||||||
| # Records | 199 | |||||||||||||||
| Variables | ||||||||||||||||
| # Input Variables | 1 | |||||||||||||||
| Input variables | ln(ppgdp) | |||||||||||||||
| Output variable | ln(ferility) | |||||||||||||||
| Parameters/Options | ||||||||||||||||
| Force constant term to zero | No | |||||||||||||||
| Show fitted values on training data | Yes | |||||||||||||||
| Show ANOVA table | Yes | |||||||||||||||
| Show standardized residuals | Yes | |||||||||||||||
| Show un-standardized residuals | No | |||||||||||||||
| Show variance covariance matrix | No | |||||||||||||||
| Perform Variable Selection | No | |||||||||||||||
| Show studentized residuals | No | |||||||||||||||
| Show deleted residuals | No | |||||||||||||||
| Show Cook's distance | No | |||||||||||||||
| Show DF fits | No | |||||||||||||||
| Show covariance ratios | No | |||||||||||||||
| Show hat matrix diagonals | No | |||||||||||||||
| Output Options Chosen | ||||||||||||||||
| Summary report of scoring on training data | ||||||||||||||||
| Detailed report of scoring on training data | ||||||||||||||||
| Lift charts on training data | ||||||||||||||||
| Model Predictors | ||||||||||||||||
| Tolerance for Entering the Model | 0 | |||||||||||||||
| Included | Excluded | |||||||||||||||
| Predictor | Criteria | Predictor | Criteria | |||||||||||||
| Intercept | 2.5472526876 | |||||||||||||||
| ln(ppgdp) | 121.3919348529 | |||||||||||||||
| Regression Model | ||||||||||||||||
| Input Variables | Coefficient | Std. Error | t-Statistic | P-Value | CI Lower | CI Upper | RSS Reduction | Residual DF | 197 | |||||||
| Intercept | 2.6655073378 | 0.1205657647 | 22.1083268954 | 2.93530254356826E-55 | 2.4277421211 | 2.9032725545 | 165.6020594861 | R² | 0.5259850345 | |||||||
| ln(ppgdp) | -0.2071497864 | 0.0140107282 | -14.7850834534 | 9.06235683202295E-34 | -0.2347800498 | -0.1795195229 | 20.6176721099 | Adjusted R² | 0.5235788671 | |||||||
| Std. Error Estimate | 0.3071114681 | |||||||||||||||
| RSS | 18.5805384058 | |||||||||||||||
| ANOVA | ||||||||||||||||
| Source | DF | SS | MS | F-Statistic | P-Value | |||||||||||
| Regression | 1 | 20.6177 | 20.6177 | 218.5987 | 0 | |||||||||||
| Error | 197 | 18.5805 | 0.0943 | |||||||||||||
| Total | 198 | 39.1982 | 20.712 | |||||||||||||
| Training Data Scoring - Summary Report | ||||||||||||||||
| Total sum of squared errors | RMS Error | Average Error | ||||||||||||||
| 18.5805384058 | 0.3055642972 | 4.43531308832663E-16 |
lifeExpFOnGroup
| group | other | africa | lifeExpF | ||||||||||
| other | 1 | 0 | 49.49 | SUMMARY OUTPUT | |||||||||
| other | 1 | 0 | 80.4 | ||||||||||
| africa | 0 | 1 | 75 | Regression Statistics | |||||||||
| africa | 0 | 1 | 53.17 | Multiple R | 0.7868134043 | ||||||||
| other | 1 | 0 | 81.1 | R Square | 0.6190753331 | ||||||||
| other | 1 | 0 | 79.89 | Adjusted R Square | 0.6151883467 | ||||||||
| other | 1 | 0 | 77.33 | Standard Error | 6.2801061827 | ||||||||
| other | 1 | 0 | 77.75 | Observations | 199 | ||||||||
| oecd | 0 | 0 | 84.27 | ||||||||||
| oecd | 0 | 0 | 83.55 | ANOVA | |||||||||
| other | 1 | 0 | 73.66 | df | SS | MS | F | Significance F | |||||
| other | 1 | 0 | 78.85 | Regression | 2 | 12563.0314933582 | 6281.5157466791 | 159.2687161617 | 8.36048455455694E-42 | ||||
| other | 1 | 0 | 76.06 | Residual | 196 | 7730.187798459 | 39.4397336656 | ||||||
| other | 1 | 0 | 70.23 | Total | 198 | 20293.2192918173 | |||||||
| other | 1 | 0 | 80.26 | ||||||||||
| other | 1 | 0 | 76.37 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| oecd | 0 | 0 | 82.81 | Intercept | 82.4464516129 | 1.1279403677 | 73.0946900864 | 3.54078776531392E-144 | 80.2219939182 | 84.6709093076 | 80.2219939182 | 84.6709093076 | |
| other | 1 | 0 | 77.81 | other | -7.1197084195 | 1.2709066366 | -5.6020703761 | 0.000000071 | -9.6261157864 | -4.6133010527 | -9.6261157864 | -4.6133010527 | |
| africa | 0 | 1 | 58.66 | africa | -22.674187462 | 1.4199983772 | -15.9677558973 | 2.58294591624273E-37 | -25.4746247964 | -19.8737501276 | -25.4746247964 | -19.8737501276 | |
| other | 1 | 0 | 82.3 | ||||||||||
| other | 1 | 0 | 69.84 | ||||||||||
| other | 1 | 0 | 69.4 | ||||||||||
| other | 1 | 0 | 78.4 | ||||||||||
| africa | 0 | 1 | 51.34 | ||||||||||
| other | 1 | 0 | 77.41 | ||||||||||
| other | 1 | 0 | 80.64 | ||||||||||
| other | 1 | 0 | 77.12 | ||||||||||
| africa | 0 | 1 | 57.02 | ||||||||||
| africa | 0 | 1 | 52.58 | ||||||||||
| other | 1 | 0 | 65.1 | ||||||||||
| africa | 0 | 1 | 53.56 | ||||||||||
| oecd | 0 | 0 | 83.49 | ||||||||||
| africa | 0 | 1 | 77.7 | ||||||||||
| other | 1 | 0 | 83.8 | ||||||||||
| africa | 0 | 1 | 51.3 | ||||||||||
| africa | 0 | 1 | 51.61 | ||||||||||
| oecd | 0 | 0 | 82.35 | ||||||||||
| other | 1 | 0 | 75.61 | ||||||||||
| other | 1 | 0 | 77.69 | ||||||||||
| africa | 0 | 1 | 63.18 | ||||||||||
| africa | 0 | 1 | 59.33 | ||||||||||
| other | 1 | 0 | 76.2454672362 | ||||||||||
| other | 1 | 0 | 81.99 | ||||||||||
| africa | 0 | 1 | 57.71 | ||||||||||
| other | 1 | 0 | 80.37 | ||||||||||
| other | 1 | 0 | 81.33 | ||||||||||
| other | 1 | 0 | 82.14 | ||||||||||
| oecd | 0 | 0 | 81 | ||||||||||
| africa | 0 | 1 | 50.56 | ||||||||||
| oecd | 0 | 0 | 81.37 | ||||||||||
| africa | 0 | 1 | 60.04 | ||||||||||
| other | 1 | 0 | 78.2 | ||||||||||
| other | 1 | 0 | 76.57 | ||||||||||
| other | 1 | 0 | 64.2 | ||||||||||
| other | 1 | 0 | 78.91 | ||||||||||
| africa | 0 | 1 | 75.52 | ||||||||||
| other | 1 | 0 | 77.09 | ||||||||||
| africa | 0 | 1 | 52.91 | ||||||||||
| africa | 0 | 1 | 64.41 | ||||||||||
| oecd | 0 | 0 | 79.95 | ||||||||||
| africa | 0 | 1 | 61.59 | ||||||||||
| other | 1 | 0 | 72.27 | ||||||||||
| oecd | 0 | 0 | 83.28 | ||||||||||
| oecd | 0 | 0 | 84.9 | ||||||||||
| other | 1 | 0 | 78.07 | ||||||||||
| africa | 0 | 1 | 64.32 | ||||||||||
| africa | 0 | 1 | 60.3 | ||||||||||
| other | 1 | 0 | 77.31 | ||||||||||
| oecd | 0 | 0 | 82.99 | ||||||||||
| africa | 0 | 1 | 65.8 | ||||||||||
| oecd | 0 | 0 | 82.58 | ||||||||||
| other | 1 | 0 | 71.6 | ||||||||||
| other | 1 | 0 | 77.72 | ||||||||||
| other | 1 | 0 | 75.1 | ||||||||||
| africa | 0 | 1 | 56.39 | ||||||||||
| africa | 0 | 1 | 50.4 | ||||||||||
| other | 1 | 0 | 73.45 | ||||||||||
| other | 1 | 0 | 63.87 | ||||||||||
| other | 1 | 0 | 75.92 | ||||||||||
| other | 1 | 0 | 86.35 | ||||||||||
| oecd | 0 | 0 | 78.47 | ||||||||||
| other | 1 | 0 | 83.77 | ||||||||||
| other | 1 | 0 | 67.62 | ||||||||||
| other | 1 | 0 | 71.8 | ||||||||||
| other | 1 | 0 | 75.28 | ||||||||||
| other | 1 | 0 | 72.6 | ||||||||||
| oecd | 0 | 0 | 83.17 | ||||||||||
| oecd | 0 | 0 | 84.19 | ||||||||||
| oecd | 0 | 0 | 84.62 | ||||||||||
| other | 1 | 0 | 75.98 | ||||||||||
| oecd | 0 | 0 | 87.12 | ||||||||||
| other | 1 | 0 | 75.17 | ||||||||||
| other | 1 | 0 | 72.84 | ||||||||||
| africa | 0 | 1 | 59.16 | ||||||||||
| other | 1 | 0 | 63.1 | ||||||||||
| other | 1 | 0 | 75.89 | ||||||||||
| other | 1 | 0 | 72.36 | ||||||||||
| other | 1 | 0 | 69.42 | ||||||||||
| other | 1 | 0 | 78.51 | ||||||||||
| other | 1 | 0 | 75.07 | ||||||||||
| africa | 0 | 1 | 48.11 | ||||||||||
| africa | 0 | 1 | 58.59 | ||||||||||
| africa | 0 | 1 | 77.86 | ||||||||||
| other | 1 | 0 | 78.28 | ||||||||||
| oecd | 0 | 0 | 82.67 | ||||||||||
| other | 1 | 0 | 83.8 | ||||||||||
| africa | 0 | 1 | 68.61 | ||||||||||
| africa | 0 | 1 | 55.17 | ||||||||||
| other | 1 | 0 | 76.86 | ||||||||||
| other | 1 | 0 | 78.7 | ||||||||||
| africa | 0 | 1 | 53.14 | ||||||||||
| other | 1 | 0 | 82.29 | ||||||||||
| other | 1 | 0 | 70.6 | ||||||||||
| africa | 0 | 1 | 60.95 | ||||||||||
| africa | 0 | 1 | 76.89 | ||||||||||
| oecd | 0 | 0 | 79.64 | ||||||||||
| other | 1 | 0 | 70.17 | ||||||||||
| other | 1 | 0 | 73.48 | ||||||||||
| other | 1 | 0 | 72.83 | ||||||||||
| other | 1 | 0 | 77.37 | ||||||||||
| africa | 0 | 1 | 74.86 | ||||||||||
| africa | 0 | 1 | 51.81 | ||||||||||
| other | 1 | 0 | 67.87 | ||||||||||
| africa | 0 | 1 | 63.04 | ||||||||||
| other | 1 | 0 | 57.1 | ||||||||||
| other | 1 | 0 | 70.05 | ||||||||||
| other | 1 | 0 | 79.86 | ||||||||||
| oecd | 0 | 0 | 82.79 | ||||||||||
| other | 1 | 0 | 80.49 | ||||||||||
| oecd | 0 | 0 | 82.77 | ||||||||||
| other | 1 | 0 | 77.45 | ||||||||||
| africa | 0 | 1 | 55.77 | ||||||||||
| africa | 0 | 1 | 53.38 | ||||||||||
| other | 1 | 0 | 72.12 | ||||||||||
| oecd | 0 | 0 | 83.47 | ||||||||||
| other | 1 | 0 | 76.44 | ||||||||||
| other | 1 | 0 | 66.88 | ||||||||||
| other | 1 | 0 | 72.1 | ||||||||||
| other | 1 | 0 | 74.81 | ||||||||||
| other | 1 | 0 | 79.07 | ||||||||||
| other | 1 | 0 | 65.52 | ||||||||||
| other | 1 | 0 | 74.91 | ||||||||||
| other | 1 | 0 | 76.9 | ||||||||||
| other | 1 | 0 | 72.57 | ||||||||||
| oecd | 0 | 0 | 80.56 | ||||||||||
| oecd | 0 | 0 | 82.76 | ||||||||||
| other | 1 | 0 | 83.2 | ||||||||||
| other | 1 | 0 | 78.24 | ||||||||||
| other | 1 | 0 | 83.95 | ||||||||||
| other | 1 | 0 | 77.95 | ||||||||||
| other | 1 | 0 | 75.01 | ||||||||||
| africa | 0 | 1 | 57.13 | ||||||||||
| other | 1 | 0 | 77.54 | ||||||||||
| other | 1 | 0 | 76.02 | ||||||||||
| africa | 0 | 1 | 66.48 | ||||||||||
| other | 1 | 0 | 75.57 | ||||||||||
| africa | 0 | 1 | 60.92 | ||||||||||
| other | 1 | 0 | 77.05 | ||||||||||
| africa | 0 | 1 | 78 | ||||||||||
| africa | 0 | 1 | 48.87 | ||||||||||
| other | 1 | 0 | 83.71 | ||||||||||
| oecd | 0 | 0 | 79.53 | ||||||||||
| oecd | 0 | 0 | 82.84 | ||||||||||
| other | 1 | 0 | 70 | ||||||||||
| africa | 0 | 1 | 53.38 | ||||||||||
| africa | 0 | 1 | 54.09 | ||||||||||
| other | 1 | 0 | 84.76 | ||||||||||
| other | 1 | 0 | 78.4 | ||||||||||
| other | 1 | 0 | 74.73 | ||||||||||
| africa | 0 | 1 | 63.82 | ||||||||||
| other | 1 | 0 | 74.18 | ||||||||||
| africa | 0 | 1 | 48.54 | ||||||||||
| oecd | 0 | 0 | 83.65 | ||||||||||
| oecd | 0 | 0 | 84.71 | ||||||||||
| other | 1 | 0 | 77.72 | ||||||||||
| other | 1 | 0 | 71.23 | ||||||||||
| africa | 0 | 1 | 60.31 | ||||||||||
| other | 1 | 0 | 77.14 | ||||||||||
| other | 1 | 0 | 77.76 | ||||||||||
| africa | 0 | 1 | 59.4 | ||||||||||
| other | 1 | 0 | 75.38 | ||||||||||
| other | 1 | 0 | 73.82 | ||||||||||
| africa | 0 | 1 | 77.05 | ||||||||||
| oecd | 0 | 0 | 76.61 | ||||||||||
| other | 1 | 0 | 69.4 | ||||||||||
| other | 1 | 0 | 65.1 | ||||||||||
| africa | 0 | 1 | 55.44 | ||||||||||
| other | 1 | 0 | 74.58 | ||||||||||
| other | 1 | 0 | 78.02 | ||||||||||
| oecd | 0 | 0 | 82.42 | ||||||||||
| oecd | 0 | 0 | 81.31 | ||||||||||
| other | 1 | 0 | 80.66 | ||||||||||
| other | 1 | 0 | 71.9 | ||||||||||
| other | 1 | 0 | 73.58 | ||||||||||
| other | 1 | 0 | 77.73 | ||||||||||
| other | 1 | 0 | 77.44 | ||||||||||
| other | 1 | 0 | 67.66 | ||||||||||
| africa | 0 | 1 | 50.04 | ||||||||||
| africa | 0 | 1 | 52.72 |
lifeExpOnGroup&ln(ppgdp)
| group | other | africa | ln( | ppgdp | ) | lifeExpF | ||||||||
| other | 1 | 0 | 6.2126060958 | 49.49 | SUMMARY OUTPUT | |||||||||
| other | 1 | 0 | 8.209906872 | 80.4 | ||||||||||
| africa | 0 | 1 | 8.4058146034 | 75 | Regression Statistics | |||||||||
| africa | 0 | 1 | 8.3714503994 | 53.17 | Multiple R | 0.8655396724 | ||||||||
| other | 1 | 0 | 9.5288013758 | 81.1 | R Square | 0.7491589244 | ||||||||
| other | 1 | 0 | 9.122830689 | 79.89 | Adjusted R Square | 0.745299831 | ||||||||
| other | 1 | 0 | 8.0165488949 | 77.33 | Standard Error | 5.1092540244 | ||||||||
| other | 1 | 0 | 10.0367720397 | 77.75 | Observations | 199 | ||||||||
| oecd | 0 | 0 | 10.9528903391 | 84.27 | ||||||||||
| oecd | 0 | 0 | 10.7179404457 | 83.55 | ANOVA | |||||||||
| other | 1 | 0 | 8.637213722 | 73.66 | df | SS | MS | F | Significance F | |||||
| other | 1 | 0 | 10.0195624635 | 78.85 | Regression | 3 | 15202.846338057 | 5067.615446019 | 194.1282143666 | 2.67925530778766E-58 | ||||
| other | 1 | 0 | 9.8083028649 | 76.06 | Residual | 195 | 5090.3729537603 | 26.104476686 | ||||||
| other | 1 | 0 | 6.5078745492 | 70.23 | Total | 198 | 20293.2192918173 | |||||||
| other | 1 | 0 | 9.5817177042 | 80.26 | ||||||||||
| other | 1 | 0 | 8.6485722695 | 76.37 | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| oecd | 0 | 0 | 10.6877269388 | 82.81 | Intercept | 49.5292409403 | 3.3995538651 | 14.5693355379 | 5.14239177668032E-33 | 42.824627035 | 56.2338548457 | 42.824627035 | 56.2338548457 | |
| other | 1 | 0 | 8.4108989066 | 77.81 | other | -1.5346826968 | 1.1736824055 | -1.3075791966 | 0.192555616 | -3.8494238919 | 0.7800584983 | -3.8494238919 | 0.7800584983 | |
| africa | 0 | 1 | 6.608135569 | 58.66 | africa | -12.1703652569 | 1.5574485782 | -7.8142966819 | 0 | -15.2419716525 | -9.0987588613 | -15.2419716525 | -9.0987588613 | |
| other | 1 | 0 | 11.4363111237 | 82.3 | ln(ppgdp) | 3.1773199909 | 0.315959718 | 10.0560919945 | 1.97277857411405E-19 | 2.554182955 | 3.8004570267 | 2.554182955 | 3.8004570267 | |
| other | 1 | 0 | 7.6242282848 | 69.84 | ||||||||||
| other | 1 | 0 | 7.5897909548 | 69.4 | ||||||||||
| other | 1 | 0 | 8.4068648007 | 78.4 | ||||||||||
| africa | 0 | 1 | 8.9096270943 | 51.34 | ||||||||||
| other | 1 | 0 | 9.2794559026 | 77.41 | ||||||||||
| other | 1 | 0 | 10.3935266251 | 80.64 | ||||||||||
| other | 1 | 0 | 8.7585852218 | 77.12 | ||||||||||
| africa | 0 | 1 | 6.253251722 | 57.02 | ||||||||||
| africa | 0 | 1 | 5.1738872882 | 52.58 | ||||||||||
| other | 1 | 0 | 6.6811055883 | 65.1 | ||||||||||
| africa | 0 | 1 | 7.095561766 | 53.56 | ||||||||||
| oecd | 0 | 0 | 10.7442117106 | 83.49 | ||||||||||
| africa | 0 | 1 | 8.0845624152 | 77.7 | ||||||||||
| other | 1 | 0 | 10.9516465448 | 83.8 | ||||||||||
| africa | 0 | 1 | 6.1110237822 | 51.3 | ||||||||||
| africa | 0 | 1 | 6.5894765326 | 51.61 | ||||||||||
| oecd | 0 | 0 | 9.3832595311 | 82.35 | ||||||||||
| other | 1 | 0 | 8.3788502418 | 75.61 | ||||||||||
| other | 1 | 0 | 8.7359752452 | 77.69 | ||||||||||
| africa | 0 | 1 | 6.602045004 | 63.18 | ||||||||||
| africa | 0 | 1 | 7.8879968593 | 59.33 | ||||||||||
| other | 1 | 0 | 9.4101825425 | 76.2454672362 | ||||||||||
| other | 1 | 0 | 8.9494689926 | 81.99 | ||||||||||
| africa | 0 | 1 | 7.0510760984 | 57.71 | ||||||||||
| other | 1 | 0 | 9.5338359172 | 80.37 | ||||||||||
| other | 1 | 0 | 8.6489930859 | 81.33 | ||||||||||
| other | 1 | 0 | 10.2528865912 | 82.14 | ||||||||||
| oecd | 0 | 0 | 9.8436738518 | 81 | ||||||||||
| africa | 0 | 1 | 5.3013128755 | 50.56 | ||||||||||
| oecd | 0 | 0 | 10.9300702206 | 81.37 | ||||||||||
| africa | 0 | 1 | 7.1566445467 | 60.04 | ||||||||||
| other | 1 | 0 | 8.8566324506 | 78.2 | ||||||||||
| other | 1 | 0 | 8.5555288977 | 76.57 | ||||||||||
| other | 1 | 0 | 6.5597568705 | 64.2 | ||||||||||
| other | 1 | 0 | 8.3120368951 | 78.91 | ||||||||||
| africa | 0 | 1 | 7.8837101716 | 75.52 | ||||||||||
| other | 1 | 0 | 8.1390319178 | 77.09 | ||||||||||
| africa | 0 | 1 | 9.7322483589 | 52.91 | ||||||||||
| africa | 0 | 1 | 6.061689992 | 64.41 | ||||||||||
| oecd | 0 | 0 | 9.5564375683 | 79.95 | ||||||||||
| africa | 0 | 1 | 5.7825936551 | 61.59 | ||||||||||
| other | 1 | 0 | 8.1734908807 | 72.27 | ||||||||||
| oecd | 0 | 0 | 10.7032826697 | 83.28 | ||||||||||
| oecd | 0 | 0 | 10.5852173016 | 84.9 | ||||||||||
| other | 1 | 0 | 10.1133026736 | 78.07 | ||||||||||
| africa | 0 | 1 | 9.4309848031 | 64.32 | ||||||||||
| africa | 0 | 1 | 6.3614751742 | 60.3 | ||||||||||
| other | 1 | 0 | 7.8936840075 | 77.31 | ||||||||||
| oecd | 0 | 0 | 10.5930558365 | 82.99 | ||||||||||
| africa | 0 | 1 | 7.1953373464 | 65.8 | ||||||||||
| oecd | 0 | 0 | 10.1850433979 | 82.58 | ||||||||||
| other | 1 | 0 | 10.4714314227 | 71.6 | ||||||||||
| other | 1 | 0 | 8.9131465392 | 77.72 | ||||||||||
| other | 1 | 0 | 7.9663438655 | 75.1 | ||||||||||
| africa | 0 | 1 | 6.0579542884 | 56.39 | ||||||||||
| africa | 0 | 1 | 6.2904574107 | 50.4 | ||||||||||
| other | 1 | 0 | 8.0050333446 | 73.45 | ||||||||||
| other | 1 | 0 | 6.4178754197 | 63.87 | ||||||||||
| other | 1 | 0 | 7.6139173966 | 75.92 | ||||||||||
| other | 1 | 0 | 10.3679665742 | 86.35 | ||||||||||
| oecd | 0 | 0 | 9.4637415105 | 78.47 | ||||||||||
| other | 1 | 0 | 10.5784198447 | 83.77 | ||||||||||
| other | 1 | 0 | 7.2487885269 | 67.62 | ||||||||||
| other | 1 | 0 | 7.989323133 | 71.8 | ||||||||||
| other | 1 | 0 | 8.56161191 | 75.28 | ||||||||||
| other | 1 | 0 | 6.7895346476 | 72.6 | ||||||||||
| oecd | 0 | 0 | 10.7411743745 | 83.17 | ||||||||||
| oecd | 0 | 0 | 10.2857386211 | 84.19 | ||||||||||
| oecd | 0 | 0 | 10.4304945489 | 84.62 | ||||||||||
| other | 1 | 0 | 8.4967863816 | 75.98 | ||||||||||
| oecd | 0 | 0 | 10.672226782 | 87.12 | ||||||||||
| other | 1 | 0 | 8.3996026372 | 75.17 | ||||||||||
| other | 1 | 0 | 9.1233326313 | 72.84 | ||||||||||
| africa | 0 | 1 | 6.6868592002 | 59.16 | ||||||||||
| other | 1 | 0 | 7.2917924397 | 63.1 | ||||||||||
| other | 1 | 0 | 10.7239367635 | 75.89 | ||||||||||
| other | 1 | 0 | 6.7631918278 | 72.36 | ||||||||||
| other | 1 | 0 | 6.9542571126 | 69.42 | ||||||||||
| other | 1 | 0 | 9.274535084 | 78.51 | ||||||||||
| other | 1 | 0 | 9.1360154532 | 75.07 | ||||||||||
| africa | 0 | 1 | 6.8882666024 | 48.11 | ||||||||||
| africa | 0 | 1 | 5.3872435757 | 58.59 | ||||||||||
| africa | 0 | 1 | 9.3343970206 | 77.86 | ||||||||||
| other | 1 | 0 | 9.303420795 | 78.28 | ||||||||||
| oecd | 0 | 0 | 11.5626237881 | 82.67 | ||||||||||
| other | 1 | 0 | 10.8195822652 | 83.8 | ||||||||||
| africa | 0 | 1 | 6.0447683191 | 68.61 | ||||||||||
| africa | 0 | 1 | 5.8788556027 | 55.17 | ||||||||||
| other | 1 | 0 | 9.0327436356 | 76.86 | ||||||||||
| other | 1 | 0 | 8.4520144654 | 78.7 | ||||||||||
| africa | 0 | 1 | 6.3949276525 | 53.14 | ||||||||||
| other | 1 | 0 | 9.8832440281 | 82.29 | ||||||||||
| other | 1 | 0 | 8.0292373817 | 70.6 | ||||||||||
| africa | 0 | 1 | 7.0309458895 | 60.95 | ||||||||||
| africa | 0 | 1 | 8.9210970815 | 76.89 | ||||||||||
| oecd | 0 | 0 | 9.1161066126 | 79.64 | ||||||||||
| other | 1 | 0 | 7.8929002061 | 70.17 | ||||||||||
| other | 1 | 0 | 7.3937552813 | 73.48 | ||||||||||
| other | 1 | 0 | 7.7172177519 | 72.83 | ||||||||||
| other | 1 | 0 | 8.7810640128 | 77.37 | ||||||||||
| africa | 0 | 1 | 7.9603236291 | 74.86 | ||||||||||
| africa | 0 | 1 | 6.0100409327 | 51.81 | ||||||||||
| other | 1 | 0 | 6.7755943754 | 67.87 | ||||||||||
| africa | 0 | 1 | 8.5418272657 | 63.04 | ||||||||||
| other | 1 | 0 | 8.7307065206 | 57.1 | ||||||||||
| other | 1 | 0 | 6.281705842 | 70.05 | ||||||||||
| other | 1 | 0 | 9.9194150341 | 79.86 | ||||||||||
| oecd | 0 | 0 | 10.7559797561 | 82.79 | ||||||||||
| other | 1 | 0 | 10.4721904983 | 80.49 | ||||||||||
| oecd | 0 | 0 | 10.3850522197 | 82.77 | ||||||||||
| other | 1 | 0 | 7.0316529156 | 77.45 | ||||||||||
| africa | 0 | 1 | 5.8796946463 | 55.77 | ||||||||||
| africa | 0 | 1 | 7.1227053553 | 53.38 | ||||||||||
| other | 1 | 0 | 6.2225762681 | 72.12 | ||||||||||
| oecd | 0 | 0 | 11.3455559669 | 83.47 | ||||||||||
| other | 1 | 0 | 9.9422754797 | 76.44 | ||||||||||
| other | 1 | 0 | 6.9109501699 | 66.88 | ||||||||||
| other | 1 | 0 | 9.2893178972 | 72.1 | ||||||||||
| other | 1 | 0 | 7.5063170171 | 74.81 | ||||||||||
| other | 1 | 0 | 8.9377439369 | 79.07 | ||||||||||
| other | 1 | 0 | 7.2643102157 | 65.52 | ||||||||||
| other | 1 | 0 | 7.9269996323 | 74.91 | ||||||||||
| other | 1 | 0 | 8.5961337535 | 76.9 | ||||||||||
| other | 1 | 0 | 7.6686078359 | 72.57 | ||||||||||
| oecd | 0 | 0 | 9.4143581869 | 80.56 | ||||||||||
| oecd | 0 | 0 | 9.9729016686 | 82.76 | ||||||||||
| other | 1 | 0 | 10.1834272298 | 83.2 | ||||||||||
| other | 1 | 0 | 11.1899325724 | 78.24 | ||||||||||
| other | 1 | 0 | 9.9547603467 | 83.95 | ||||||||||
| other | 1 | 0 | 8.925640515 | 77.95 | ||||||||||
| other | 1 | 0 | 9.2448770552 | 75.01 | ||||||||||
| africa | 0 | 1 | 6.2772072402 | 57.13 | ||||||||||
| other | 1 | 0 | 8.8064390405 | 77.54 | ||||||||||
| other | 1 | 0 | 8.1147136221 | 76.02 | ||||||||||
| africa | 0 | 1 | 7.1571901643 | 66.48 | ||||||||||
| other | 1 | 0 | 9.6700347935 | 75.57 | ||||||||||
| africa | 0 | 1 | 6.9399320107 | 60.92 | ||||||||||
| other | 1 | 0 | 8.5415345228 | 77.05 | ||||||||||
| africa | 0 | 1 | 9.3457974094 | 78 | ||||||||||
| africa | 0 | 1 | 5.8627785395 | 48.87 | ||||||||||
| other | 1 | 0 | 10.6870031772 | 83.71 | ||||||||||
| oecd | 0 | 0 | 9.6788428751 | 79.53 | ||||||||||
| oecd | 0 | 0 | 10.048012049 | 82.84 | ||||||||||
| other | 1 | 0 | 7.0846454458 | 70 | ||||||||||
| africa | 0 | 1 | 4.7431914839 | 53.38 | ||||||||||
| africa | 0 | 1 | 8.8894185977 | 54.09 | ||||||||||
| other | 1 | 0 | 10.3268842576 | 84.76 | ||||||||||
| other | 1 | 0 | 7.7728790243 | 78.4 | ||||||||||
| other | 1 | 0 | 8.7277296057 | 74.73 | ||||||||||
| africa | 0 | 1 | 7.50928047 | 63.82 | ||||||||||
| other | 1 | 0 | 8.8562335561 | 74.18 | ||||||||||
| africa | 0 | 1 | 8.1050659404 | 48.54 | ||||||||||
| oecd | 0 | 0 | 10.7976594568 | 83.65 | ||||||||||
| oecd | 0 | 0 | 11.1401240427 | 84.71 | ||||||||||
| other | 1 | 0 | 7.9832695164 | 77.72 | ||||||||||
| other | 1 | 0 | 6.704414355 | 71.23 | ||||||||||
| africa | 0 | 1 | 6.2461067655 | 60.31 | ||||||||||
| other | 1 | 0 | 8.3971701488 | 77.14 | ||||||||||
| other | 1 | 0 | 8.4365903269 | 77.76 | ||||||||||
| africa | 0 | 1 | 6.2626360674 | 59.4 | ||||||||||
| other | 1 | 0 | 8.1727573291 | 75.38 | ||||||||||
| other | 1 | 0 | 9.6293861769 | 73.82 | ||||||||||
| africa | 0 | 1 | 8.3480879136 | 77.05 | ||||||||||
| oecd | 0 | 0 | 9.2198054366 | 76.61 | ||||||||||
| other | 1 | 0 | 8.4310904924 | 69.4 | ||||||||||
| other | 1 | 0 | 8.0668980674 | 65.1 | ||||||||||
| africa | 0 | 1 | 6.2324480166 | 55.44 | ||||||||||
| other | 1 | 0 | 8.0179667035 | 74.58 | ||||||||||
| other | 1 | 0 | 10.5872079402 | 78.02 | ||||||||||
| oecd | 0 | 0 | 10.5003110399 | 82.42 | ||||||||||
| oecd | 0 | 0 | 10.7481942015 | 81.31 | ||||||||||
| other | 1 | 0 | 9.388687374 | 80.66 | ||||||||||
| other | 1 | 0 | 7.2635398266 | 71.9 | ||||||||||
| other | 1 | 0 | 7.9941262812 | 73.58 | ||||||||||
| other | 1 | 0 | 9.5106449444 | 77.73 | ||||||||||
| other | 1 | 0 | 7.0755552393 | 77.44 | ||||||||||
| other | 1 | 0 | 7.2704520552 | 67.66 | ||||||||||
| africa | 0 | 1 | 7.1210908893 | 50.04 | ||||||||||
| africa | 0 | 1 | 6.3510602216 | 52.72 |
Regression Statistics
Multiple R0.72108
R Square0.519956
Adjusted R Square0.51752
Standard Error0.93049
Observations199
ANOVA
dfSSMSFSignificance F
Regression1184.7462184.7462213.37933.16E-33
Residual197170.56480.865811
Total198355.3109
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept8.0096690.36529121.926799.34E-557.2892858.730053
ln(ppgdp)-0.620090.04245-14.60753.16E-33-0.7038-0.53637
Regression Statistics
Multiple R0.464675
R Square0.215923
Adjusted R Square0.211943
Standard Error0.394984
Observations199
ANOVA
dfSSMSFSignificance F
Regression18.4637948.46379454.250824.72E-12
Residual19730.734420.156012
Total19839.19821
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept1.0583450.03431530.842412.43E-770.9906731.126016
ppgdp-1.1E-051.52E-06-7.365524.72E-12-1.4E-05-8.2E-06
Regression Statistics
Multiple R0.725248
R Square0.525985
Adjusted R Square0.523579
Standard Error0.307111
Observations199
ANOVA
dfSSMSFSignificance F
Regression120.6176720.61767218.59879.06E-34
Residual19718.580540.094317
Total19839.19821
CoefficientsStandard Errort StatP-valueLower 95%
Intercept2.6655070.12056622.108332.94E-552.427742
ln(ppgdp)-0.207150.014011-14.78519.06E-34-0.23478