Finance reserch report based on provided data
Dennis547
Lecture_11.pptxData Analysis – 7 Functional Forms and Variable Types
FINA305/405
1
Agenda
Linear in parameters
Non-linear functional forms
Residual analysis (summary)
Dummy and categorical variables
Interaction terms (not intercept term)
Practice in Excel
2
Introduction
What is linearity or linear modle?
Nonlinearity?
Dependents on which dimension we are talking about.
3
Introduction
We want to focus on linear models. More specifically, linear in parameters (parameters are linearly combined by data)
4
Introduction
6
Introduction
In practice, non-linear functional forms (but still linear in parameters) is useful:
Help discover new insights from the data.
Deal with data analysis issues.
7
Non-linear functional forms
Is the relationship linear?
We could perform a regression of Y (or ln(Y) or Y2) on X2 (or 1/X or ln(X) or X3, etc.)… and the same estimation technique (OLS) for the equation’s parameters would hold.
How will we decide?
Theory (would the marginal effect on cig consumption of income be likely to be constant? ie. does $1 of extra income have the same effect for an unemployed smoker as a millionaire smoker?)
Graphical analysis: What does a plot of the two variables look like?
Choosing functional form
Common transformations are:
Squared (quadratic) terms
Taking natural logs (one side or both sides) – implies elasticities, not slopes, are constant.
Note: Need values > 0 to take log
Model non-linearity in the data, deal with heteroscedasticity and distribution issues, sometimes easier to explain in %
Again, to find the proper data transformation, try the following:
Plot out the data in X-Y space (scatter plot)
Scan relevant theory for any suggestions
Log-log transformation
So, data in previous slide suggest that double log model is ‘correct’ one:
Interpretation of results will be different:
Eg. A coefficient of 10 implies a 1% change in X yields a 10% change in Y
Semi-Log transformation
Y=α+ β*lnX + e
Interpretation of β : X changes by 1 per cent, Y will change by β/100 units.
Example: Family income as X in dollars and baby’s birth weight as Y in kilos.
lnY=α1+ β1*X + e1
Interpretation of β : X changes by 1 unit, Y will change by β*100 per cent.
Example: Number of hours spent on this course as X, course final grade as Y.
Quadratic transformation
Suppose we estimate the model for 3 sub-sample.
Linear relationship: β1=β2=β3
Possible function:
Cig=α+β*Income
(α>0, β>0)
Nonlinear relationship: β4≠β5≠β6
Possible function (quadratic):
Cig=α+β*Income+ γ*Income2
(α>0, β>0 and γ<0)
Residual Analysis (summary)
Plot residuals against predicted Y values.
“How well does the regression line fit through the points on the XY-plot?”
Well-fitting models have small residuals (i.e. small SSR)
“Are there any outliers which do not fit the general pattern?”
If residual is big for one observation (relative to other observations), then that observation is called an “outlier.”
Is the variance of residual homoscedastic?
Funnel or uneven distribution may be an evidence of heteroscedasticity
Quiz
Which of the following statements regarding R-squared is correct?
Which regression model would you choose if the variable you are seeking to forecast is increasing at a constant percentage rate in response to 1% change in the independent variable?
| A) | |
| B) | |
| C) | |
| D) | |
| E) |
| A) | R-squared is a measure of the degree of variability in the independent variables as a group that is explained by the regression line (or plane). |
| B) | If the R-squared value is smaller than the standard error of the regression, then the model is not significant. |
| C) | The null hypothesis that R-squared = 0 can be tested using an F-test. |
| D) | If the R-squared is low, then the model is not significant. |
| E) | A and C only. |
Dummy variables
An indicator or categorical variable is created to measure qualitative data.
Do you smoke: yes (=1) /no (=0)
Are you the only child in your family: yes (=1)/no (=0)
How do you go to Uni: Walk (=1), Public transport (=2), Drive (=3), Other (=0)
A dummy (binary) variable is a special case of indicator (categorical) variable where the variable takes on two values: 0 or 1 for each observation
How do you go to Uni: Walk (=1)/otherwise (=0)
Public transport (=1)/otherwise (=0)
Drive (=1)/otherwise (=0)
Other (=1)/otherwise (=0)
Now we have 4 dummies.
Example: Birth Weight
Dependent Variable: Birth weight
Previously, we included two independent variables:
number of cigarettes smoked by mum (continuous)
family income (continuous).
However, we may wish to include gender of child (a binary variable) as an explanatory variable.
Can we do this using multiple regression?
Setting up a dummy
We could set our dummy up as follows:
Generate a variable called ‘male’ (or gener or female)
For each observation, set values as follows:
1 if child is male
0 if female
Note in this example only one dummy variable ‘male’ is used even though there were two conditions (male and female). This is because one fewer dummy variable is constructed than conditions. The condition not explicitly represented by a dummy variable, the omitted condition, forms the basis against which the included conditions are compared.
For dual conditions (male vs. female), the coefficient is interpreted as the effect of the included condition relative to the omitted condition.
Example: Birth Weight
OLS estimates:
This is the slope estimate
on our dummy variable
Interpretations
For baby girls (D1= 0):
For baby boys (D1=1)
NOTE: The slope on “cigarettes” is
the same; the
“intercept” is
different
Graphical Illustration
5.75
7.574
7.39
Birth
Weight
# Cigarettes
7.206
Example: Wages
Suppose that we have the following data on 526 people living in the United States:
Wage: average hourly earnings
Educ: years of education
Exper: years of potential experience
Non-white: = 1 if non-white; = 0 otherwise
Female: = 1 if female; = 0 otherwise
Married: = 1 if married; = 0 otherwise
NumDep: number of dependents
Building the Model
Scan the literature on wage determination.
You will find that there are some common themes that run through the literature:
Should use experience AND (experience)2
Some authors use wage and some use ln(wage) as the dependent variable
Should control for gender and race
We are going to start with the following:
Y = WAGES (in USD per hour)
X1= EDUCATION
X2 = EXPERIENCE
D1 = FEMALE
D2 = NON-WHITE
Estimate and Evaluate
Check the significance and develop an interpretation of the results.
Education: positive and highly significant
Experience: positive and highly significant
(Experience)2: negative and highly significant
Female: negative and highly significant
Non-white: negative but NOT significant
Check R2 and F-stat
Expand the model
Add in marital status and number of dependents to our model:
Open question
Should you keep marital status and number of dependents in your model?
Interaction Terms
We might have some reason to believe that a combined impact of two or more variables might drive Y – in addition to the “main effects” of each of the variables by themselves.
To capture this effect, we can construct an “interaction term”
We can interact (=multiply) a dummy variable with another dummy variable OR a dummy variable with a continuous variable.
So, if D1 = 1, then:
But, if D1 = 0, then:
Not only do we
have different
“intercept” terms,
we now have a
different slope on X1.
Example
We have estimated the effect say of being female, and being married
What about an interaction term: woman AND married? Seems reasonable that there would be some sort of joint effect
In excel, we can create a new column called “married female”, which is a dummy variable taking the value 1 if female = 1 AND married = 1; and 0 otherwise.
What are the characteristics of individuals in the 0 category?
Create an interaction term in Excel
Estimation
34
Illustration
35
Interpretation
Hourly earnings of married female is 0.36 dollars lower than unmarried female.
Stogner (negatively) effect of “female” for married than unmarried individuals.
36
Evaluate
By every criterion, this a better model (adjusted and F-test)
Further, we see large qualitative changes:
The wage difference between men and women is no longer significant at 95%
Married, number of dependents, and being a married female are all statistically significant now
Being a married female has a large, negative, significant effect on wages
Parameter estimates and statistical significance on education, experience and experience2 remain relatively unchanged.
Understanding the interaction coefficient estimate (homework)
First, the female and married dummies create four categories of people:
Male and unmarried
Male and married
Female and unmarried
Female and married
Second, our estimated equation is Predicted wage(ln)=A + B, where
A=(0.36+0.08edu+0.04exp-0.0007expsq—0.03nonwhite-0.03.numdep)
B= -0.11female+0.27married-0.36marriedfemale
Hence,
Male and unmarried: A (B=0)
Male and married: A+0.27 (B=0.27)
Female and unmarried: A-0.11 (B=-0.11)
Female and married: A-0.2 (B=-0.11+0.27-0.36=-0.2)
Now you can compare the wages between any of the four groups. Try male and married vs. female and unmarried:
Note
People often make mistakes when applying and explaining dummy variables and interaction terms (variables).
Dummy variables can easily be used as independent variables in regression – and are often exploited to create interaction terms
You can include N – 1 number of dummies in a model, where N is the number of categories you want to capture
The “excluded category” is the one that all coefficient estimates compare against
Categorical variables
Lots of different examples
Usually arise because of the way the data were collected (eg ABS group into categories, rather than presenting exact income)
Must always leave one category out (reference/base category)
All coefficients marginal effect relative to the reference/base category
Examples
Income categories. Eg.
0 - $10000 (low)
$10001 - $40000 (median)
>$40000 (high)
Age categories
0-5 years
6-15 years
16-35 years
> 35 years
Categorical variables
Three income categories
Only two dummy variables maximum
If Income_low and Income_median are in regression (Income_high is excluded ),
the coefficient of Income_low represents the difference between Income_low and Income_high;
the coefficient of Income_median represents the difference between Income_median and Income_high.
Dummy dependent variables
What if the dependent variable is dummy (or categorical)?
Binary dependent variable, a special case of limited dependent variable
We still apply what we learned about OLS.
But the model is now called linear probability model(LPM) because the fitted value of is between 0 and 1 (ideally), just like probability.
Example
Where High Income = 1 if income > average, 0 otherwise
Where has a continuous values
Explain: 1 year increase of education will lead to *100 percentage increase of probability to have high income, holding experience constant.
Problems with LPM
Sometimes the fitted value is lager than 1 or smaller than 0.
Meaningless.
Often associated with heteroscedasticity problem
Non-normal distribution of error term.
Writing your research report
A brief introduction that defines the dependent variable and states the goals of the research
A short review of relevant previous literature and research
An explanation of the specification of the equation (model), i.e. why the particular independent variables and functional forms, the expected signs of the coefficient estimates.
A description of the data, data sources, and any irregularities with the data.
A presentation of each estimated specification, and discuss which one is the most appropriate if you have a few specifications.
A careful analysis of the regression results that includes a discussion of any econometric problems.
A short summary/conclusion that include any policy recommendations or suggestions for further research.
References and Appendix if applicable
Practice in Excel
http://www.rbnz.govt.nz/statistics/key-graphs/key-graph-house-price-values
Regression (OLS)
Functional forms and variable types
Not a linear relationship - try taking logs of X and/or Y
0
0.5
1
1.5
2
2.5
3
3.5
4
02468101214
Chart1
| 0.07514454 |
| 0.29640921 |
| 3.9213341 |
| 0.57137522 |
| 0.2123828 |
| 2.9158112 |
| 11.681007 |
| 0.22166345 |
| 1.6587597 |
| 0.62982737 |
| 3.5013892 |
| 3.604552 |
| 0.86334708 |
| 0.87835987 |
| 0.84769079 |
| 2.3326408 |
| 0.23542986 |
| 0.68949 |
| 0.87017509 |
| 0.27737136 |
| 2.4492377 |
| 1.0167623 |
| 0.67179529 |
| 3.0596516 |
| 2.2763494 |
| 1.9913621 |
| 1.6826936 |
| 3.1292622 |
| 1.859066 |
| 6.3910606 |
| 1.4128243 |
| 2.623146 |
| 2.480595 |
| 0.22395529 |
| 2.8188792 |
| 0.12407072 |
| 0.81538801 |
| 1.9892655 |
| 0.20476791 |
| 0.83599276 |
| 0.43718765 |
| 0.28923076 |
| 0.37373342 |
| 2.3702882 |
| 4.8529391 |
| 1.2813698 |
| 0.82131254 |
| 2.9661813 |
| 0.15618286 |
| 6.0886672 |
Chart2
| -2.5883418 |
| -1.2160143 |
| 1.3664319 |
| -0.55970915 |
| -1.549365 |
| 1.0701481 |
| 2.4579642 |
| -1.506595 |
| 0.50607014 |
| -0.46230951 |
| 1.2531598 |
| 1.2821975 |
| -0.14693848 |
| -0.12969889 |
| -0.16523934 |
| 0.84700102 |
| -1.4463422 |
| -0.37180308 |
| -0.13906084 |
| -1.282398 |
| 0.89577684 |
| 0.016623368 |
| -0.39780162 |
| 1.1183011 |
| 0.82257304 |
| 0.68881885 |
| 0.52039587 |
| 1.1407972 |
| 0.62007419 |
| 1.8549002 |
| 0.34559072 |
| 0.96437435 |
| 0.90849847 |
| -1.4963088 |
| 1.0363394 |
| -2.0869035 |
| -0.20409119 |
| 0.68776546 |
| -1.5858781 |
| -0.17913533 |
| -0.82739278 |
| -1.2405304 |
| -0.98421252 |
| 0.86301155 |
| 1.5795845 |
| 0.24792967 |
| -0.19685155 |
| 1.0872754 |
| -1.8567278 |
| 1.8064292 |
TEMPG
| 0.07514454 | 0.27458229 | -2.5883418 | -1.2925043 |
| 0.29640921 | 0.5323973 | -1.2160143 | -0.63036526 |
| 3.9213341 | 1.9691606 | 1.3664319 | 0.67760736 |
| 0.57137522 | 0.78234649 | -0.55970915 | -0.24545756 |
| 0.2123828 | 0.46423 | -1.549365 | -0.76737515 |
| 2.9158112 | 1.7888898 | 1.0701481 | 0.58159522 |
| 11.681007 | 3.6653881 | 2.4579642 | 1.2989342 |
| 0.22166345 | 0.4482274 | -1.506595 | -0.8024546 |
| 1.6587597 | 1.2616612 | 0.50607014 | 0.23242926 |
| 0.62982737 | 0.73493449 | -0.46230951 | -0.30797391 |
| 3.5013892 | 1.8220678 | 1.2531598 | 0.599972 |
| 3.604552 | 1.6984948 | 1.2821975 | 0.52974242 |
| 0.86334708 | 0.89414341 | -0.14693848 | -0.1118891 |
| 0.87835987 | 0.93399475 | -0.12969889 | -0.068284461 |
| 0.84769079 | 0.91190076 | -0.16523934 | -0.092224107 |
| 2.3326408 | 1.4684414 | 0.84700102 | 0.38420159 |
| 0.23542986 | 0.43802348 | -1.4463422 | -0.82548276 |
| 0.68949 | 0.89838293 | -0.37180308 | -0.10715888 |
| 0.87017509 | 0.87178488 | -0.13906084 | -0.13721259 |
| 0.27737136 | 0.4844723 | -1.282398 | -0.72469501 |
| 2.4492377 | 1.5517732 | 0.89577684 | 0.43939826 |
| 1.0167623 | 1.0594594 | 0.016623368 | 0.057758739 |
| 0.67179529 | 0.88783888 | -0.39780162 | -0.11896499 |
| 3.0596516 | 1.8638074 | 1.1183011 | 0.62262137 |
| 2.2763494 | 1.5110543 | 0.82257304 | 0.41280765 |
| 1.9913621 | 1.4751487 | 0.68881885 | 0.38875878 |
| 1.6826936 | 1.50673 | 0.52039587 | 0.40994172 |
| 3.1292622 | 1.6697603 | 1.1407972 | 0.51268009 |
| 1.859066 | 1.3237087 | 0.62007419 | 0.2804374 |
| 6.3910606 | 2.5445885 | 1.8549002 | 0.93396895 |
| 1.4128243 | 1.2229717 | 0.34559072 | 0.20128371 |
| 2.623146 | 1.7226036 | 0.96437435 | 0.54383686 |
| 2.480595 | 1.546902 | 0.90849847 | 0.43625424 |
| 0.22395529 | 0.47570928 | -1.4963088 | -0.74294836 |
| 2.8188792 | 1.6291362 | 1.0363394 | 0.48804992 |
| 0.12407072 | 0.3362827 | -2.0869035 | -1.0898031 |
| 0.81538801 | 0.87133074 | -0.20409119 | -0.13773365 |
| 1.9892655 | 1.4409171 | 0.68776546 | 0.3652798 |
| 0.20476791 | 0.48249368 | -1.5858781 | -0.72878745 |
| 0.83599276 | 0.87477139 | -0.17913533 | -0.13379269 |
| 0.43718765 | 0.68031173 | -0.82739278 | -0.38520415 |
| 0.28923076 | 0.56196972 | -1.2405304 | -0.5763073 |
| 0.37373342 | 0.58812615 | -0.98421252 | -0.53081382 |
| 2.3702882 | 1.4005141 | 0.86301155 | 0.33683938 |
| 4.8529391 | 2.4064245 | 1.5795845 | 0.87814204 |
| 1.2813698 | 1.1813111 | 0.24792967 | 0.16662491 |
| 0.82131254 | 0.89022403 | -0.19685155 | -0.11628213 |
| 2.9661813 | 1.7082946 | 1.0872754 | 0.53549556 |
| 0.15618286 | 0.42439902 | -1.8567278 | -0.85708117 |
| 6.0886672 | 2.309287 | 1.8064292 | 0.83693882 |
-1.5-1-0.500.511.5-3-2-10123
ln(X) versus ln(Y)
Chart1
| 0.07514454 |
| 0.29640921 |
| 3.9213341 |
| 0.57137522 |
| 0.2123828 |
| 2.9158112 |
| 11.681007 |
| 0.22166345 |
| 1.6587597 |
| 0.62982737 |
| 3.5013892 |
| 3.604552 |
| 0.86334708 |
| 0.87835987 |
| 0.84769079 |
| 2.3326408 |
| 0.23542986 |
| 0.68949 |
| 0.87017509 |
| 0.27737136 |
| 2.4492377 |
| 1.0167623 |
| 0.67179529 |
| 3.0596516 |
| 2.2763494 |
| 1.9913621 |
| 1.6826936 |
| 3.1292622 |
| 1.859066 |
| 6.3910606 |
| 1.4128243 |
| 2.623146 |
| 2.480595 |
| 0.22395529 |
| 2.8188792 |
| 0.12407072 |
| 0.81538801 |
| 1.9892655 |
| 0.20476791 |
| 0.83599276 |
| 0.43718765 |
| 0.28923076 |
| 0.37373342 |
| 2.3702882 |
| 4.8529391 |
| 1.2813698 |
| 0.82131254 |
| 2.9661813 |
| 0.15618286 |
| 6.0886672 |
Chart2
| -2.5883418 |
| -1.2160143 |
| 1.3664319 |
| -0.55970915 |
| -1.549365 |
| 1.0701481 |
| 2.4579642 |
| -1.506595 |
| 0.50607014 |
| -0.46230951 |
| 1.2531598 |
| 1.2821975 |
| -0.14693848 |
| -0.12969889 |
| -0.16523934 |
| 0.84700102 |
| -1.4463422 |
| -0.37180308 |
| -0.13906084 |
| -1.282398 |
| 0.89577684 |
| 0.016623368 |
| -0.39780162 |
| 1.1183011 |
| 0.82257304 |
| 0.68881885 |
| 0.52039587 |
| 1.1407972 |
| 0.62007419 |
| 1.8549002 |
| 0.34559072 |
| 0.96437435 |
| 0.90849847 |
| -1.4963088 |
| 1.0363394 |
| -2.0869035 |
| -0.20409119 |
| 0.68776546 |
| -1.5858781 |
| -0.17913533 |
| -0.82739278 |
| -1.2405304 |
| -0.98421252 |
| 0.86301155 |
| 1.5795845 |
| 0.24792967 |
| -0.19685155 |
| 1.0872754 |
| -1.8567278 |
| 1.8064292 |
TEMPG
| 0.07514454 | 0.27458229 | -2.5883418 | -1.2925043 |
| 0.29640921 | 0.5323973 | -1.2160143 | -0.63036526 |
| 3.9213341 | 1.9691606 | 1.3664319 | 0.67760736 |
| 0.57137522 | 0.78234649 | -0.55970915 | -0.24545756 |
| 0.2123828 | 0.46423 | -1.549365 | -0.76737515 |
| 2.9158112 | 1.7888898 | 1.0701481 | 0.58159522 |
| 11.681007 | 3.6653881 | 2.4579642 | 1.2989342 |
| 0.22166345 | 0.4482274 | -1.506595 | -0.8024546 |
| 1.6587597 | 1.2616612 | 0.50607014 | 0.23242926 |
| 0.62982737 | 0.73493449 | -0.46230951 | -0.30797391 |
| 3.5013892 | 1.8220678 | 1.2531598 | 0.599972 |
| 3.604552 | 1.6984948 | 1.2821975 | 0.52974242 |
| 0.86334708 | 0.89414341 | -0.14693848 | -0.1118891 |
| 0.87835987 | 0.93399475 | -0.12969889 | -0.068284461 |
| 0.84769079 | 0.91190076 | -0.16523934 | -0.092224107 |
| 2.3326408 | 1.4684414 | 0.84700102 | 0.38420159 |
| 0.23542986 | 0.43802348 | -1.4463422 | -0.82548276 |
| 0.68949 | 0.89838293 | -0.37180308 | -0.10715888 |
| 0.87017509 | 0.87178488 | -0.13906084 | -0.13721259 |
| 0.27737136 | 0.4844723 | -1.282398 | -0.72469501 |
| 2.4492377 | 1.5517732 | 0.89577684 | 0.43939826 |
| 1.0167623 | 1.0594594 | 0.016623368 | 0.057758739 |
| 0.67179529 | 0.88783888 | -0.39780162 | -0.11896499 |
| 3.0596516 | 1.8638074 | 1.1183011 | 0.62262137 |
| 2.2763494 | 1.5110543 | 0.82257304 | 0.41280765 |
| 1.9913621 | 1.4751487 | 0.68881885 | 0.38875878 |
| 1.6826936 | 1.50673 | 0.52039587 | 0.40994172 |
| 3.1292622 | 1.6697603 | 1.1407972 | 0.51268009 |
| 1.859066 | 1.3237087 | 0.62007419 | 0.2804374 |
| 6.3910606 | 2.5445885 | 1.8549002 | 0.93396895 |
| 1.4128243 | 1.2229717 | 0.34559072 | 0.20128371 |
| 2.623146 | 1.7226036 | 0.96437435 | 0.54383686 |
| 2.480595 | 1.546902 | 0.90849847 | 0.43625424 |
| 0.22395529 | 0.47570928 | -1.4963088 | -0.74294836 |
| 2.8188792 | 1.6291362 | 1.0363394 | 0.48804992 |
| 0.12407072 | 0.3362827 | -2.0869035 | -1.0898031 |
| 0.81538801 | 0.87133074 | -0.20409119 | -0.13773365 |
| 1.9892655 | 1.4409171 | 0.68776546 | 0.3652798 |
| 0.20476791 | 0.48249368 | -1.5858781 | -0.72878745 |
| 0.83599276 | 0.87477139 | -0.17913533 | -0.13379269 |
| 0.43718765 | 0.68031173 | -0.82739278 | -0.38520415 |
| 0.28923076 | 0.56196972 | -1.2405304 | -0.5763073 |
| 0.37373342 | 0.58812615 | -0.98421252 | -0.53081382 |
| 2.3702882 | 1.4005141 | 0.86301155 | 0.33683938 |
| 4.8529391 | 2.4064245 | 1.5795845 | 0.87814204 |
| 1.2813698 | 1.1813111 | 0.24792967 | 0.16662491 |
| 0.82131254 | 0.89022403 | -0.19685155 | -0.11628213 |
| 2.9661813 | 1.7082946 | 1.0872754 | 0.53549556 |
| 0.15618286 | 0.42439902 | -1.8567278 | -0.85708117 |
| 6.0886672 | 2.309287 | 1.8064292 | 0.83693882 |
lnln
YXe
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CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept 7.3900353140.050080584147.562907.2917933227.488277305
male 0.1837088920.067437942.7241180.0065280.0514173530.316000432
cigs -0.0321032260.005642629-5.6894091.55E-08-0.043172248-0.0210342
1
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2
5
1
4
2
2
3
2
2
1
1
b
b
b
b
b
a
Regression Statistics
Multiple R0.591844885
R Square0.350280368
Adjusted R Square0.344033063
Standard Error2.991096324
Observations 526
ANOVA
dfSSMSFSignificance F
Regression 52508.152557501.630556.069041.35503E-46
Residual 5204652.2617548.946657
Total 5257160.41431
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept-2.2827792260.746116766-3.0595470.002331-3.748552783-0.817005668
educ0.5546318810.05053181810.975892.37E-250.4553602850.653903477
exper0.2554458380.0349069697.3179049.61E-130.1868698270.324021849
expersq-0.0044481470.000777181-5.7234361.77E-08-0.005974947-0.002921346
female-2.1157924970.262812626-8.0505745.64E-15-2.632097472-1.599487522
nonwhite-0.1578328930.431539254-0.3657440.714705-1.0056074730.689941687
Regression Statistics
Multiple R0.59210801
R Square0.350591896
Adjusted R Square0.34181611
Standard Error2.996146523
Observations 526
ANOVA
dfSSMSFSignificance F
Regression 72510.383226358.62617539.949926.7736E-45
Residual 5184650.0310848.97689399
Total 5257160.41431
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept-2.27820.7943-2.86820.004296-3.8387-0.7178
educ0.55140.053710.26711.23E-220.44590.6569
exper0.24810.03896.37384.08E-100.17160.3245
expersq-0.00430.0009-5.06645.65E-07-0.0060-0.0026
female-2.09620.2663-7.87042.08E-14-2.6195-1.5730
nonwhite-0.14170.4343-0.32610.744443-0.99500.7116
married0.15330.30990.49460.621116-0.45560.7621
numdep-0.00190.1151-0.01610.98714-0.22790.2242
1
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2
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Y
b
a
+
=
Regression Statistics
Multiple R0.656942
R Square0.431573
Adjusted R Square0.422777
Standard Error0.403837
Observations 526
ANOVA
dfSSMSFSignificance F
Regression 864.015087268.00188590749.065899.21533E-59
Residual 51784.314675520.163084479
Total 525148.3297628
CoefficientsStandard Errort StatP-valueLower 95%Upper 95%
Intercept0.3617560.108565253.332153850.0009230.1484728420.57503939
educ0.0770640.00725190410.62667785.44E-240.0628168250.09131047
exper0.037280.0052462357.1060669613.98E-120.0269735360.04758665
expersq-0.0006890.000115033-5.98943753.95E-09-0.000914973-0.000463
female-0.1052470.057596728-1.827316740.068228-0.2183998670.00790494
nonwhite-0.0255090.058640403-0.435000930.663743-0.1407113970.08969414
married0.2694250.0576450354.6738628893.78E-060.1561776860.38267229
numdep-0.0328020.015624704-2.099344210.036271-0.063497348-0.0021059
married female-0.3644540.073993106-4.925506641.13E-06-0.509817655-0.2190894
