BUSI ForecastX
djcvie
busi405_week4.xlsHints
| BUSI/BMIS 405 | ||||
| Chapter 4: Introuduction to Forecasting with Regression Methods | ||||
| 1. Homework: Exercises 4, 6, 9, 11, and 14 | ||||
| Exercise 4: | ||||
| a. t-ratio=coefficient/standard error (p. 183)(correction H1: β ≠ 0, p.183) | ||||
| The rule of thumb for significance testing is if the absolute value of t-ratio is greater than 2 | ||||
| then, the coefficient is statisically significant which means the coefficient is significantly different from zero. | ||||
| For example, t-ratio for "Constant" is 3.04 which is greater than 2. Therefore, the coefficient of 20,720 is | ||||
| significantly different from zero. | ||||
| If we know the sample size of this problem, we could use table 2.5 for t-test. | ||||
| b. It is R-squared right below the table | ||||
| c. Substitute 20 into EXP in the following equation | ||||
| Salary = 20,720 + 805 (EXP) for point estimate | ||||
| the approximate 95 percent confidence interval estimates would be | ||||
| point estimate ± 2 (SEE) (p. 184) | ||||
| SEE is the standard erro of the estimate which is right under R-squared value | ||||
| Exercise 6: | ||||
| a. The equation is | ||||
| Booking = b0 + b1(Income) | ||||
| Booking is the dependent variable and Income is the independent variable | ||||
| To obtian the regression eq;uation using Forecast X: | ||||
| First, highlight the data for "Bookings" and "Income." Do not highlight "Location" | ||||
| Open Forecast X > Forecast Method > Choose "Multiple Regression" under "Forecast Technique" > Report > Audit>Finish | ||||
| b. Please see pp. 178-184. The three steps of evaluation are summarized | ||||
| at the end of page 183 and the beginning of page 184. | ||||
| c. For point and interval estimates, please refer to exercise 4c. | ||||
| Exercise 9: | ||||
| a. Naïve forecat for 2008 Q1 = actual value in 2007 Q4 | ||||
| b. Highlight the following data. | ||||
| Period | FURN ($Billions) | |||
| Mar-98 | 98.1 | |||
| Jun-98 | 96.8 | |||
| Sep-98 | 96 | |||
| Dec-98 | 95 | |||
| Mar-99 | 93.2 | |||
| Jun-99 | 95.1 | |||
| Sep-99 | 96.2 | |||
| Dec-99 | 98.4 | |||
| Mar-00 | 100.7 | |||
| Jun-00 | 104.4 | |||
| Sep-00 | 108.1 | |||
| Dec-00 | 111.1 | |||
| Mar-01 | 114.3 | |||
| Jun-01 | 117.2 | |||
| Sep-01 | 119.4 | |||
| Dec-01 | 122.7 | |||
| Mar-02 | 125.9 | |||
| Jun-02 | 129.3 | |||
| Sep-02 | 132.2 | |||
| Dec-02 | 136.6 | |||
| Mar-03 | 137.4 | |||
| Jun-03 | 141.4 | |||
| Sep-03 | 145.3 | |||
| Dec-03 | 147.7 | |||
| Mar-04 | 148.8 | |||
| Jun-04 | 150.2 | |||
| Sep-04 | 153.4 | |||
| Dec-04 | 154.2 | |||
| Mar-05 | 159.8 | |||
| Jun-05 | 164.4 | |||
| Sep-05 | 166.2 | |||
| Dec-05 | 169.7 | |||
| Mar-06 | 173.7 | |||
| Jun-06 | 175.5 | |||
| Sep-06 | 175 | |||
| Dec-06 | 175.7 | |||
| Mar-07 | 181.4 | |||
| Jun-07 | 180 | |||
| Sep-07 | 179.7 | |||
| Dec-07 | 176.3 | |||
| Open Forecast X > Forecast Method > Choose "Trend (Linear) Regression" under "Forecast Technique" | ||||
| c. Please refer to exercise 6b. | ||||
| d. Substitue "Time" value into the regression equation for trend forecast. | ||||
| Exercise 10: | ||||
| c. Percentage error in forecat = (actual value - point estimate) / actual value = forecast error / actual value | ||||
| Exercise 11: | ||||
| You will arrange the data in two columns. One for "Year" and one for "Population" for regression analysis | ||||
| Year | Population | |||
| Open Forecast X > Forecast Method > Choose "Trend (Linear) Regression" | ||||
| Exercise 14: | ||||
| a.For trend forecat, open Forecast X > Forecast Method > Choose "Trend (Linear) Regression" | ||||
| b. To reseasonalize the data, time the value with the corresponding seasonal index | ||||
| For example, for Jan-07, actual shoe store sales SSS=SASSS x 0.74 = 2,317 x 0.74=1,714.58 |
QS. 4
| Variable | Coefficient | Standard Error | T Ratio | R-squared | 0.684 | ||
| Constant | 20720 | 6820 | 3.04 | n | 105 | ||
| EXP | 805 | 258 | 3.12 | Standard error of the estimate | 2000 | ||
| A. | The t-ratio is 3.12. | Yes, because the t-ratio is greater than 2 which means the coeffecient is statisically significant | |||||
| B. | 68.40% | ||||||
| C. | Point Estimate | 36820 | |||||
| 20 | Years | ||||||
| D. | 40820 | 32820 |
QS. 6
| Location | Bookings | Income | |||||||||||||||||
| 1 | 1,098 | 43,299 | B. As income increases, so do sales which makes it positive. | ||||||||||||||||
| 2 | 1,131 | 45,021 | C. | ||||||||||||||||
| 3 | 1,120 | 40,290 | |||||||||||||||||
| 4 | 1,142 | 41,893 | |||||||||||||||||
| 5 | 971 | 30,620 | |||||||||||||||||
| 6 | 1,403 | 48,105 | |||||||||||||||||
| 7 | 855 | 27,482 | |||||||||||||||||
| 8 | 1,054 | 33,025 | |||||||||||||||||
| 9 | 1,081 | 34,687 | |||||||||||||||||
| 10 | 982 | 28,725 | |||||||||||||||||
| 11 | 1,098 | 37,892 | |||||||||||||||||
| 12 | 1,387 | 46,198 | |||||||||||||||||
| 13 | 39,020 | ||||||||||||||||||
| Multiple Regression -- Result Formula | Multiple Regression -- Result Formula | ||||||||||||||||||
| Bookings = 371.68 + ( (Income) * 0.019381 ) | Bookings = 350.62 + ( (Income) * 0.01766 ) | ||||||||||||||||||
| Forecast -- Multiple Regression Selected | Forecast -- Multiple Regression Selected | ||||||||||||||||||
| Forecast | Forecast | ||||||||||||||||||
| Date | Monthly | Quarterly | Annual | Date | Annual | ||||||||||||||
| May-2015 | 1,110.04 | Apr-2016 | 1,039.72 | ||||||||||||||||
| Jun-2015 | 1,110.04 | 2,220.08 | Apr-2017 | 1,039.72 | |||||||||||||||
| Jul-2015 | 1,110.04 | Apr-2018 | 1,039.72 | ||||||||||||||||
| Aug-2015 | 1,110.04 | Apr-2019 | 1,039.72 | ||||||||||||||||
| Sep-2015 | 1,110.04 | 3,330.12 | Apr-2020 | 1,039.72 | |||||||||||||||
| Oct-2015 | 1,110.04 | Apr-2021 | 1,039.72 | ||||||||||||||||
| Nov-2015 | 1,110.04 | Apr-2022 | 1,039.72 | ||||||||||||||||
| Dec-2015 | 1,110.04 | 3,330.12 | 8,880.31 | Apr-2023 | 1,039.72 | ||||||||||||||
| Jan-2016 | 1,110.04 | Apr-2024 | 1,039.72 | ||||||||||||||||
| Feb-2016 | 1,110.04 | Apr-2025 | 1,039.72 | ||||||||||||||||
| Mar-2016 | 1,110.04 | 3,330.12 | Apr-2026 | 1,039.72 | |||||||||||||||
| Apr-2016 | 1,110.04 | Apr-2027 | 1,039.72 | ||||||||||||||||
| Total | 13,320.46 | Total | 12,476.60 | ||||||||||||||||
| Avg | 1,110.04 | 3,052.61 | 8,880.31 | Avg | 1,039.72 | ||||||||||||||
| Max | 1,110.04 | 3,330.12 | 8,880.31 | Max | 1,039.72 | ||||||||||||||
| Min | 1,110.04 | 2,220.08 | 8,880.31 | Min | 1,039.72 | ||||||||||||||
| Summary Comments | Summary Comments | ||||||||||||||||||
| The forecast has an average error of | 5.21% | The forecast has an average error of | 7.95% | ||||||||||||||||
| The data has a standard deviation of | 156.42 | The data has a standard deviation of | 342.39 | ||||||||||||||||
| The forecast exceeds the accuracy of a simple average by | 77.30% | The forecast exceeds the accuracy of a simple average by | 12.29% | ||||||||||||||||
| Audit Trail - Summary Analysis | Audit Trail - Summary Analysis | ||||||||||||||||||
| Audit Trail - Historical Versus Fitted Analysis | Audit Trail - Historical Versus Fitted Analysis | ||||||||||||||||||
| Series:Bookings | Series:Bookings | ||||||||||||||||||
| Dates | Original Data | Fitted Data | Error | Series % Change | Forecast % Change | Cumulative Error | Cumulative MAPE | Dates | Original Data | Fitted Data | Error | Series % Change | Forecast % Change | Cumulative Error | Cumulative MAPE | ||||
| May-2014 | 1,098.00 | 1,210.87 | -112.87 | -112.87 | 10.28% | Apr-2003 | 1,098.00 | 1,115.28 | -17.28 | -17.28 | 1.57% | ||||||||
| Jun-2014 | 1,131.00 | 1,244.25 | -113.25 | 3.01% | 2.76% | -113.06 | 7.64% | Apr-2004 | 1,131.00 | 1,145.69 | -14.69 | 3.01% | 2.73% | -15.99 | 1.11% | ||||
| Jul-2014 | 1,120.00 | 1,152.55 | -32.55 | -0.97% | -7.37% | -86.22 | 5.42% | Apr-2005 | 1,120.00 | 1,062.14 | 57.86 | -0.97% | -7.29% | 8.63 | 1.32% | ||||
| Aug-2014 | 1,142.00 | 1,183.62 | -41.62 | 1.96% | 2.70% | -75.07 | 4.29% | Apr-2006 | 1,142.00 | 1,090.45 | 51.55 | 1.96% | 2.67% | 19.36 | 1.27% | ||||
| Sep-2014 | 971.00 | 965.13 | 5.87 | -14.97% | -18.46% | -58.88 | 3.46% | Apr-2007 | 971.00 | 891.37 | 79.63 | -14.97% | -18.26% | 31.41 | 1.34% | ||||
| Oct-2014 | 1,403.00 | 1,304.02 | 98.98 | 44.49% | 35.11% | -32.57 | 3.08% | Apr-2008 | 1,403.00 | 1,200.16 | 202.84 | 44.49% | 34.64% | 59.98 | 1.52% | ||||
| Nov-2014 | 855.00 | 904.32 | -49.32 | -39.06% | -30.65% | -34.97 | 2.76% | Apr-2009 | 855.00 | 835.96 | 19.04 | -39.06% | -30.35% | 54.13 | 1.35% | ||||
| Dec-2014 | 1,054.00 | 1,011.75 | 42.25 | 23.27% | 11.88% | -25.31 | 2.47% | Apr-2010 | 1,054.00 | 933.84 | 120.16 | 23.27% | 11.71% | 62.39 | 1.36% | ||||
| Jan-2015 | 1,081.00 | 1,043.96 | 37.04 | 2.56% | 3.18% | -18.38 | 2.24% | Apr-2011 | 1,081.00 | 963.20 | 117.80 | 2.56% | 3.14% | 68.54 | 1.34% | ||||
| Feb-2015 | 982.00 | 928.41 | 53.59 | -9.16% | -11.07% | -11.19 | 2.07% | Apr-2012 | 982.00 | 857.91 | 124.09 | -9.16% | -10.93% | 74.10 | 1.33% | ||||
| Mar-2015 | 1,098.00 | 1,106.08 | -8.08 | 11.81% | 19.14% | -10.90 | 1.89% | Apr-2013 | 1,098.00 | 1,019.80 | 78.20 | 11.81% | 18.87% | 74.47 | 1.27% | ||||
| Apr-2015 | 1,387.00 | 1,267.06 | 119.94 | 26.32% | 14.55% | 0.00 | 1.79% | Apr-2014 | 1,387.00 | 1,166.48 | 220.52 | 26.32% | 14.38% | 86.64 | 1.28% | ||||
| Avg | 1,110.17 | 1,110.17 | 0.00 | 4.48% | 1.98% | -48.29 | 3.95% | Apr-2015 | 0.00 | 1,039.72 | -1,039.72 | -100.00% | -10.87% | -0.00 | 1.18% | ||||
| Max | 1,403.00 | 1,304.02 | 119.94 | 44.49% | 35.11% | 0.00 | 10.28% | Avg | 1,024.77 | 1,024.77 | -0.00 | -4.23% | 0.87% | 38.95 | 1.33% | ||||
| Min | 855.00 | 904.32 | -113.25 | -39.06% | -30.65% | -113.06 | 1.79% | Max | 1,403.00 | 1,200.16 | 220.52 | 44.49% | 34.64% | 86.64 | 1.57% | ||||
| StDev | 156.42 | 137.52 | 74.53 | 22.33% | 18.41% | 39.99 | 2.63% | Min | 0.00 | 835.96 | -1,039.72 | -100.00% | -30.35% | -17.28 | 1.11% | ||||
| Var | 24,467.06 | 18,912.39 | 5,554.67 | 4.99% | 3.39% | 1,598.83 | 0.07% | StDev | 342.39 | 120.06 | 320.66 | 36.92% | 17.74% | 36.43 | 0.12% | ||||
| Median | 1,098.00 | 1,129.31 | -1.10 | 2.56% | 2.76% | -33.77 | 2.92% | Var | 117,233.53 | 14,413.80 | 102,819.73 | 13.63% | 3.15% | 1,327.32 | 0.00% | ||||
| Median | 1,098.00 | 1,039.72 | 78.20 | 2.26% | 2.70% | 54.13 | 1.33% | ||||||||||||
| Audit Trail -- ANOVA Table (Multiple Regression Selected) | |||||||||||||||||||
| Source of variation | SS | df | MS | SEE | Audit Trail -- ANOVA Table (Multiple Regression Selected) | ||||||||||||||
| Regression | 208,036.32 | 1 | 208,036.32 | Source of variation | SS | df | MS | SEE | |||||||||||
| Error | 61,101.35 | 10 | 6,110.13 | 78.17 | Regression | 172,965.55 | 1 | 172,965.55 | |||||||||||
| Total | 269,137.67 | 11 | Error | 1,233,836.76 | 11 | 112,166.98 | 334.91 | ||||||||||||
| Total | 1,406,802.31 | 12 | |||||||||||||||||
| Audit Trail -- Coefficient Table (Multiple Regression Selected) | |||||||||||||||||||
| Series Description | Included in model | Coefficient | Standard error | T-test | P-value | Elasticity | Overall F-test | Audit Trail -- Coefficient Table (Multiple Regression Selected) | |||||||||||
| Bookings | Dependent | 371.68 | 128.56 | 2.89 | 0.02 | 34.05 | Series Description | Included in model | Coefficient | Standard error | T-test | P-value | Elasticity | Overall F-test | |||||
| Income | Yes | 0.02 | 0.00 | 5.84 | 0.00 | 0.67 | Bookings | Dependent | 350.62 | 550.77 | 0.64 | 0.54 | 1.54 | ||||||
| Income | Yes | 0.02 | 0.01 | 1.24 | 0.24 | 0.66 | |||||||||||||
| Audit Trail -- Correlation Coefficient Table | |||||||||||||||||||
| Series Description | Included in model | Bookings | Income | Audit Trail -- Correlation Coefficient Table | |||||||||||||||
| Bookings | Dependent | 1.00 | 0.88 | Series Description | Included in model | Bookings | Income | ||||||||||||
| Income | Yes | 0.88 | 1.00 | Bookings | Dependent | 1.00 | 0.35 | ||||||||||||
| Income | Yes | 0.35 | 1.00 | ||||||||||||||||
| Audit Trail - Statistics | |||||||||||||||||||
| Audit Trail - Statistics | |||||||||||||||||||
| Accuracy Measures | Value | Forecast Statistics | Value | ||||||||||||||||
| MAPE | 5.21% | Durbin Watson (1) | 1.12 | Accuracy Measures | Value | Forecast Statistics | Value | ||||||||||||
| R-Square | 77.30% | Mean | 1,110.17 | MAPE | 7.95% | Durbin Watson (1) | 1.36 | ||||||||||||
| Mean Absolute Error | 59.61 | Standard Deviation | 156.42 | R-Square | 12.29% | Mean | 1,024.77 | ||||||||||||
| Root Mean Square Error | 71.36 | Root Mean Square Error | 308.08 | Standard Deviation | 342.39 | ||||||||||||||
| Method Statistics | Value | Method Statistics | Value | ||||||||||||||||
| Method Selected | Multiple Regression | Method Selected | Multiple Regression | ||||||||||||||||
| ForecastX Configuration Parameters | ForecastX Configuration Parameters | ||||||||||||||||||
| Item | Value | Item | Value | ||||||||||||||||
| Data range selected | [BUSI405_Week4_Fvelazquez.xls]QS. 6'!$A$1:$C$13 | Data range selected | [BUSI405_Week4_Fvelazquez.xls]QS. 6'!$A$1:$C$14 | ||||||||||||||||
| Time scale for data | Monthly | Time scale for data | Annual | ||||||||||||||||
| Periods to forecast | 12.00 | Periods to forecast | 12.00 | ||||||||||||||||
| Seasonal Length | Seasonal Length | ||||||||||||||||||
| Replace Outliers Activated | No | Replace Outliers Activated | No | ||||||||||||||||
| Replace Outliers Standard Deviations | Replace Outliers Standard Deviations | ||||||||||||||||||
| Replace Outliers Forecasting Technique | Replace Outliers Forecasting Technique | ||||||||||||||||||
| Replace Missing Values | No | Replace Missing Values | No | ||||||||||||||||
| Replace Missing Values (Lower Limit) | Replace Missing Values (Lower Limit) | ||||||||||||||||||
| Replace Missing Values (Upper Limit) | Replace Missing Values (Upper Limit) | ||||||||||||||||||
| Remove Leading Zeroes | No | Remove Leading Zeroes | No | ||||||||||||||||
| Remove Trailing Zeroes | No | Remove Trailing Zeroes | No | ||||||||||||||||
| Use Holdback Evaluation | No | Use Holdback Evaluation | No | ||||||||||||||||
| Holdback Evaluation Period | Holdback Evaluation Period | ||||||||||||||||||
| Apply Tracking Signal | No | Apply Tracking Signal | No | ||||||||||||||||
| Apply Tracking Signal (Under Forecast Percentage) | Apply Tracking Signal (Under Forecast Percentage) | ||||||||||||||||||
| Apply Tracking Signal (Over Forecast Percentage) | Apply Tracking Signal (Over Forecast Percentage) | ||||||||||||||||||
| Forecast Method Selected | Multiple Regression | Forecast Method Selected | Multiple Regression | ||||||||||||||||
| Report Details | Report Details | ||||||||||||||||||
| Run Date: 4/29/2015 10:28:24 PM | Run Date: 4/29/2015 10:34:04 PM | ||||||||||||||||||
| Author: djcavie | Author: djcavie | ||||||||||||||||||
| Note: | Note: |
QS. 6
| 41787.9363773148 | 1210.8707690603 | 41787.9363773148 | |
| 41818.9363773148 | 1244.2455276345 | 41818.9363773148 | |
| 41848.9363773148 | 1152.5521578234 | 41848.9363773148 | |
| 41879.9363773148 | 1183.6205306425 | 41879.9363773148 | |
| 41910.9363773148 | 965.134088478 | 41910.9363773148 | |
| 41940.9363773148 | 1304.0177433389 | 41940.9363773148 | |
| 41971.9363773148 | 904.3152775571 | 41971.9363773148 | |
| 42001.9363773148 | 1011.7463384031 | 42001.9363773148 | |
| 42032.9363773148 | 1043.9582134033 | 42032.9363773148 | |
| 42063.9363773148 | 928.4063489321 | 42063.9363773148 | |
| 42092.9363773148 | 1106.0755776486 | 42092.9363773148 | |
| 42123.9363773148 | 1267.0574270781 | 1267.0574270781 | 42123.9363773148 |
| 42153.9363773148 | 1110.0385398926 | 42153.9363773148 | |
| 42184.9363773148 | 1110.0385398926 | 42184.9363773148 | |
| 42214.9363773148 | 1110.0385398926 | 42214.9363773148 | |
| 42245.9363773148 | 1110.0385398926 | 42245.9363773148 | |
| 42276.9363773148 | 1110.0385398926 | 42276.9363773148 | |
| 42306.9363773148 | 1110.0385398926 | 42306.9363773148 | |
| 42337.9363773148 | 1110.0385398926 | 42337.9363773148 | |
| 42367.9363773148 | 1110.0385398926 | 42367.9363773148 | |
| 42398.9363773148 | 1110.0385398926 | 42398.9363773148 | |
| 42429.9363773148 | 1110.0385398926 | 42429.9363773148 | |
| 42458.9363773148 | 1110.0385398926 | 42458.9363773148 | |
| 42489.9363773148 | 1110.0385398926 | 42489.9363773148 |
Actual
Forecast
Fitted Values
Bookings
1098
1131
1120
1142
971
1403
855
1054
1081
982
1098
1387
701
QS.9
| 37740.9403240741 | 1115.2836133028 | 37740.9403240741 | |
| 38106.9403240741 | 1145.6941636165 | 38106.9403240741 | |
| 38471.9403240741 | 1062.1446203332 | 38471.9403240741 | |
| 38836.9403240741 | 1090.453628552 | 38836.9403240741 | |
| 39201.9403240741 | 891.3722501051 | 39201.9403240741 | |
| 39567.9403240741 | 1200.1576579064 | 39567.9403240741 | |
| 39932.9403240741 | 835.9551148646 | 39932.9403240741 | |
| 40297.9403240741 | 933.8445924421 | 40297.9403240741 | |
| 40662.9403240741 | 963.1955416995 | 40662.9403240741 | |
| 41028.9403240741 | 857.906516746 | 41028.9403240741 | |
| 41393.9403240741 | 1019.7958981195 | 41393.9403240741 | |
| 41758.9403240741 | 1166.4800043361 | 41758.9403240741 | |
| 42123.9403240741 | 1039.7163979765 | 1039.7163979765 | 42123.9403240741 |
| 42489.9403240741 | 1039.7163979765 | 42489.9403240741 | |
| 42854.9403240741 | 1039.7163979765 | 42854.9403240741 | |
| 43219.9403240741 | 1039.7163979765 | 43219.9403240741 | |
| 43584.9403240741 | 1039.7163979765 | 43584.9403240741 | |
| 43950.9403240741 | 1039.7163979765 | 43950.9403240741 | |
| 44315.9403240741 | 1039.7163979765 | 44315.9403240741 | |
| 44680.9403240741 | 1039.7163979765 | 44680.9403240741 | |
| 45045.9403240741 | 1039.7163979765 | 45045.9403240741 | |
| 45411.9403240741 | 1039.7163979765 | 45411.9403240741 | |
| 45776.9403240741 | 1039.7163979765 | 45776.9403240741 | |
| 46141.9403240741 | 1039.7163979765 | 46141.9403240741 | |
| 46506.9403240741 | 1039.7163979765 | 46506.9403240741 |
Actual
Forecast
Fitted Values
Bookings
1098
1131
1120
1142
971
1403
855
1054
1081
982
1098
1387
0
701
QS.10
| Time | Period | FURN ($Billions) | A. | Period | Naïve Forecast | C. | ||||||||||
| 1 | Mar-98 | 98.1 | 2008Q1 | 176.3 | ||||||||||||
| 2 | Jun-98 | 96.8 | ||||||||||||||
| 3 | Sep-98 | 96 | B. | |||||||||||||
| 4 | Dec-98 | 95 | ||||||||||||||
| 5 | Mar-99 | 93.2 | ||||||||||||||
| 6 | Jun-99 | 95.1 | ||||||||||||||
| 7 | Sep-99 | 96.2 | ||||||||||||||
| 8 | Dec-99 | 98.4 | ||||||||||||||
| 9 | Mar-00 | 100.7 | ||||||||||||||
| 10 | Jun-00 | 104.4 | ||||||||||||||
| 11 | Sep-00 | 108.1 | ||||||||||||||
| 12 | Dec-00 | 111.1 | ||||||||||||||
| 13 | Mar-01 | 114.3 | ||||||||||||||
| 14 | Jun-01 | 117.2 | ||||||||||||||
| 15 | Sep-01 | 119.4 | ||||||||||||||
| 16 | Dec-01 | 122.7 | ||||||||||||||
| 17 | Mar-02 | 125.9 | ||||||||||||||
| 18 | Jun-02 | 129.3 | ||||||||||||||
| 19 | Sep-02 | 132.2 | Forecast -- Trend (Linear) Regression Selected | |||||||||||||
| 20 | Dec-02 | 136.6 | Forecast | |||||||||||||
| 21 | Mar-03 | 137.4 | Date | Quarterly | Annual | |||||||||||
| 22 | Jun-03 | 141.4 | Jul-2015 | 189.03 | ||||||||||||
| 23 | Sep-03 | 145.3 | Oct-2015 | 191.61 | 380.65 | |||||||||||
| 24 | Dec-03 | 147.7 | Jan-2016 | 194.19 | ||||||||||||
| 25 | Mar-04 | 148.8 | Apr-2016 | 196.77 | ||||||||||||
| 26 | Jun-04 | 150.2 | Jul-2016 | 199.35 | ||||||||||||
| 27 | Sep-04 | 153.4 | Oct-2016 | 201.93 | 792.24 | |||||||||||
| 28 | Dec-04 | 154.2 | Jan-2017 | 204.51 | ||||||||||||
| 29 | Mar-05 | 159.8 | Apr-2017 | 207.09 | ||||||||||||
| 30 | Jun-05 | 164.4 | Jul-2017 | 209.67 | ||||||||||||
| 31 | Sep-05 | 166.2 | Oct-2017 | 212.24 | 833.50 | |||||||||||
| 32 | Dec-05 | 169.7 | Jan-2018 | 214.82 | ||||||||||||
| 33 | Mar-06 | 173.7 | Apr-2018 | 217.40 | ||||||||||||
| 34 | Jun-06 | 175.5 | Total | 2,438.61 | ||||||||||||
| 35 | Sep-06 | 175 | Avg | 203.22 | 668.80 | |||||||||||
| 36 | Dec-06 | 175.7 | Max | 217.40 | 833.50 | |||||||||||
| 37 | Mar-07 | 181.4 | Min | 189.03 | 380.65 | |||||||||||
| 38 | Jun-07 | 180 | ||||||||||||||
| 39 | Sep-07 | 179.7 | Summary Comments | |||||||||||||
| 40 | Dec-07 | 176.3 | The forecast has an average error of | 2.59% | ||||||||||||
| The data has a standard deviation of | 30.43 | |||||||||||||||
| The forecast exceeds the accuracy of a simple average by | 98.15% | |||||||||||||||
| Audit Trail - Summary Analysis | ||||||||||||||||
| Audit Trail - Historical Versus Fitted Analysis | ||||||||||||||||
| Series:FURN ($Billions) | ||||||||||||||||
| Dates | Original Data | Fitted Data | Error | Series % Change | Forecast % Change | Cumulative Error | Cumulative MAPE | |||||||||
| Jul-2005 | 98.10 | 85.87 | 12.23 | 12.23 | 12.47% | |||||||||||
| Oct-2005 | 96.80 | 88.45 | 8.35 | -1.33% | 3.00% | 10.29 | 8.39% | |||||||||
| Jan-2006 | 96.00 | 91.03 | 4.97 | -0.83% | 2.92% | 8.52 | 6.17% | |||||||||
| Apr-2006 | 95.00 | 93.61 | 1.39 | -1.04% | 2.83% | 6.74 | 4.72% | |||||||||
| Jul-2006 | 93.20 | 96.19 | -2.99 | -1.89% | 2.76% | 4.79 | 3.90% | |||||||||
| Oct-2006 | 95.10 | 98.77 | -3.67 | 2.04% | 2.68% | 3.38 | 3.36% | |||||||||
| Jan-2007 | 96.20 | 101.35 | -5.15 | 1.16% | 2.61% | 2.16 | 2.99% | |||||||||
| Apr-2007 | 98.40 | 103.92 | -5.52 | 2.29% | 2.54% | 1.20 | 2.70% | |||||||||
| Jul-2007 | 100.70 | 106.50 | -5.80 | 2.34% | 2.48% | 0.42 | 2.47% | |||||||||
| Oct-2007 | 104.40 | 109.08 | -4.68 | 3.67% | 2.42% | -0.09 | 2.27% | |||||||||
| Jan-2008 | 108.10 | 111.66 | -3.56 | 3.54% | 2.36% | -0.40 | 2.09% | |||||||||
| Apr-2008 | 111.10 | 114.24 | -3.14 | 2.78% | 2.31% | -0.63 | 1.94% | |||||||||
| Jul-2008 | 114.30 | 116.82 | -2.52 | 2.88% | 2.26% | -0.78 | 1.80% | |||||||||
| Oct-2008 | 117.20 | 119.40 | -2.20 | 2.54% | 2.21% | -0.88 | 1.68% | |||||||||
| Jan-2009 | 119.40 | 121.98 | -2.58 | 1.88% | 2.16% | -0.99 | 1.58% | |||||||||
| Apr-2009 | 122.70 | 124.56 | -1.86 | 2.76% | 2.11% | -1.05 | 1.49% | |||||||||
| Jul-2009 | 125.90 | 127.14 | -1.24 | 2.61% | 2.07% | -1.06 | 1.40% | |||||||||
| Oct-2009 | 129.30 | 129.71 | -0.41 | 2.70% | 2.03% | -1.02 | 1.33% | |||||||||
| Jan-2010 | 132.20 | 132.29 | -0.09 | 2.24% | 1.99% | -0.97 | 1.26% | |||||||||
| Apr-2010 | 136.60 | 134.87 | 1.73 | 3.33% | 1.95% | -0.84 | 1.20% | |||||||||
| Jul-2010 | 137.40 | 137.45 | -0.05 | 0.59% | 1.91% | -0.80 | 1.14% | |||||||||
| Oct-2010 | 141.40 | 140.03 | 1.37 | 2.91% | 1.88% | -0.70 | 1.09% | |||||||||
| Jan-2011 | 145.30 | 142.61 | 2.69 | 2.76% | 1.84% | -0.55 | 1.05% | |||||||||
| Apr-2011 | 147.70 | 145.19 | 2.51 | 1.65% | 1.81% | -0.43 | 1.01% | |||||||||
| Jul-2011 | 148.80 | 147.77 | 1.03 | 0.74% | 1.78% | -0.37 | 0.97% | |||||||||
| Oct-2011 | 150.20 | 150.35 | -0.15 | 0.94% | 1.75% | -0.36 | 0.93% | |||||||||
| Jan-2012 | 153.40 | 152.93 | 0.47 | 2.13% | 1.72% | -0.33 | 0.90% | |||||||||
| Apr-2012 | 154.20 | 155.51 | -1.31 | 0.52% | 1.69% | -0.36 | 0.86% | |||||||||
| Jul-2012 | 159.80 | 158.08 | 1.72 | 3.63% | 1.66% | -0.29 | 0.84% | |||||||||
| Oct-2012 | 164.40 | 160.66 | 3.74 | 2.88% | 1.63% | -0.16 | 0.81% | |||||||||
| Jan-2013 | 166.20 | 163.24 | 2.96 | 1.09% | 1.61% | -0.06 | 0.79% | |||||||||
| Apr-2013 | 169.70 | 165.82 | 3.88 | 2.11% | 1.58% | 0.07 | 0.76% | |||||||||
| Jul-2013 | 173.70 | 168.40 | 5.30 | 2.36% | 1.56% | 0.22 | 0.74% | |||||||||
| Oct-2013 | 175.50 | 170.98 | 4.52 | 1.04% | 1.53% | 0.35 | 0.72% | |||||||||
| Jan-2014 | 175.00 | 173.56 | 1.44 | -0.28% | 1.51% | 0.38 | 0.70% | |||||||||
| Apr-2014 | 175.70 | 176.14 | -0.44 | 0.40% | 1.49% | 0.36 | 0.68% | |||||||||
| Jul-2014 | 181.40 | 178.72 | 2.68 | 3.24% | 1.46% | 0.42 | 0.67% | |||||||||
| Oct-2014 | 180.00 | 181.30 | -1.30 | -0.77% | 1.44% | 0.38 | 0.65% | |||||||||
| Jan-2015 | 179.70 | 183.87 | -4.17 | -0.17% | 1.42% | 0.26 | 0.63% | |||||||||
| Apr-2015 | 176.30 | 186.45 | -10.15 | -1.89% | 1.40% | 0.00 | 0.62% | |||||||||
| Avg | 136.16 | 136.16 | 0.00 | 1.53% | 2.01% | 0.98 | 2.04% | |||||||||
| Max | 181.40 | 186.45 | 12.23 | 3.67% | 3.00% | 12.23 | 12.47% | |||||||||
| Min | 93.20 | 85.87 | -10.15 | -1.89% | 1.40% | -1.06 | 0.62% | |||||||||
| StDev | 30.43 | 30.15 | 4.14 | 1.59% | 0.46% | 3.15 | 2.34% | |||||||||
| Var | 926.19 | 909.04 | 17.15 | 0.03% | 0.00% | 9.92 | 0.05% | |||||||||
| Median | 137.00 | 136.16 | -0.12 | 2.11% | 1.91% | -0.12 | 1.17% | |||||||||
| Audit Trail -- ANOVA Table (Trend (Linear) Regression Selected) | ||||||||||||||||
| Source of variation | SS | df | MS | SEE | ||||||||||||
| Regression | 35,452.56 | 1 | 35,452.56 | |||||||||||||
| Error | 668.71 | 38 | 17.60 | 4.19 | ||||||||||||
| Total | 36,121.27 | 39 | ||||||||||||||
| Audit Trail -- Coefficient Table (Trend (Linear) Regression Selected) | ||||||||||||||||
| Name | Value | Standard Error | T-test | P-value | Elasticity | Overall F-test | ||||||||||
| Intercept | 83.29 | 1.35 | 61.61 | 0.00 | 2,014.61 | |||||||||||
| Slope | 2.58 | 0.06 | 44.88 | 0.00 | 0.39 | |||||||||||
| Audit Trail -- Correlation Coefficient Table | ||||||||||||||||
| Series | Period | FURN ($Billions) | ||||||||||||||
| Period | 0.00 | 0.00 | ||||||||||||||
| FURN ($Billions) | 0.00 | 1.00 | ||||||||||||||
| Audit Trail - Statistics | ||||||||||||||||
| Accuracy Measures | Value | Forecast Statistics | Value | |||||||||||||
| MAPE | 2.59% | Durbin Watson (1) | 0.27 | |||||||||||||
| R-Square | 98.15% | Mean | 136.16 | |||||||||||||
| Root Mean Square Error | 4.09 | Standard Deviation | 30.43 | |||||||||||||
| Method Statistics | Value | |||||||||||||||
| Method Selected | Trend (Linear) Regression | |||||||||||||||
| ForecastX Configuration Parameters | ||||||||||||||||
| Item | Value | |||||||||||||||
| Data range selected | [BUSI405_Week4_Fvelazquez.xls]QS.9!$A$1:$C$41 | |||||||||||||||
| Time scale for data | Quarterly | |||||||||||||||
| Periods to forecast | 12.00 | |||||||||||||||
| Seasonal Length | ||||||||||||||||
| Replace Outliers Activated | No | |||||||||||||||
| Replace Outliers Standard Deviations | ||||||||||||||||
| Replace Outliers Forecasting Technique | ||||||||||||||||
| Replace Missing Values | No | |||||||||||||||
| Replace Missing Values (Lower Limit) | ||||||||||||||||
| Replace Missing Values (Upper Limit) | ||||||||||||||||
| Remove Leading Zeroes | Yes | |||||||||||||||
| Remove Trailing Zeroes | No | |||||||||||||||
| Use Holdback Evaluation | No | |||||||||||||||
| Holdback Evaluation Period | ||||||||||||||||
| Apply Tracking Signal | No | |||||||||||||||
| Apply Tracking Signal (Under Forecast Percentage) | ||||||||||||||||
| Apply Tracking Signal (Over Forecast Percentage) | ||||||||||||||||
| Forecast Method Selected | Trend (Linear) Regression | |||||||||||||||
| Report Details | ||||||||||||||||
| Run Date: 4/29/2015 10:42:35 PM | ||||||||||||||||
| Author: djcavie | ||||||||||||||||
| Note: |
End month of quarter
QS.10
| 38562.9462268519 | 85.8709756098 | 38562.9462268519 | |
| 38654.9462268519 | 88.4500281426 | 38654.9462268519 | |
| 38746.9462268519 | 91.0290806754 | 38746.9462268519 | |
| 38836.9462268519 | 93.6081332083 | 38836.9462268519 | |
| 38927.9462268519 | 96.1871857411 | 38927.9462268519 | |
| 39019.9462268519 | 98.7662382739 | 39019.9462268519 | |
| 39111.9462268519 | 101.3452908068 | 39111.9462268519 | |
| 39201.9462268519 | 103.9243433396 | 39201.9462268519 | |
| 39292.9462268519 | 106.5033958724 | 39292.9462268519 | |
| 39384.9462268519 | 109.0824484053 | 39384.9462268519 | |
| 39476.9462268519 | 111.6615009381 | 39476.9462268519 | |
| 39567.9462268519 | 114.2405534709 | 39567.9462268519 | |
| 39658.9462268519 | 116.8196060038 | 39658.9462268519 | |
| 39750.9462268519 | 119.3986585366 | 39750.9462268519 | |
| 39842.9462268519 | 121.9777110694 | 39842.9462268519 | |
| 39932.9462268519 | 124.5567636023 | 39932.9462268519 | |
| 40023.9462268519 | 127.1358161351 | 40023.9462268519 | |
| 40115.9462268519 | 129.7148686679 | 40115.9462268519 | |
| 40207.9462268519 | 132.2939212007 | 40207.9462268519 | |
| 40297.9462268519 | 134.8729737336 | 40297.9462268519 | |
| 40388.9462268519 | 137.4520262664 | 40388.9462268519 | |
| 40480.9462268519 | 140.0310787992 | 40480.9462268519 | |
| 40572.9462268519 | 142.6101313321 | 40572.9462268519 | |
| 40662.9462268519 | 145.1891838649 | 40662.9462268519 | |
| 40753.9462268519 | 147.7682363977 | 40753.9462268519 | |
| 40845.9462268519 | 150.3472889306 | 40845.9462268519 | |
| 40937.9462268519 | 152.9263414634 | 40937.9462268519 | |
| 41028.9462268519 | 155.5053939962 | 41028.9462268519 | |
| 41119.9462268519 | 158.0844465291 | 41119.9462268519 | |
| 41211.9462268519 | 160.6634990619 | 41211.9462268519 | |
| 41303.9462268519 | 163.2425515947 | 41303.9462268519 | |
| 41393.9462268519 | 165.8216041276 | 41393.9462268519 | |
| 41484.9462268519 | 168.4006566604 | 41484.9462268519 | |
| 41576.9462268519 | 170.9797091932 | 41576.9462268519 | |
| 41668.9462268519 | 173.5587617261 | 41668.9462268519 | |
| 41758.9462268519 | 176.1378142589 | 41758.9462268519 | |
| 41849.9462268519 | 178.7168667917 | 41849.9462268519 | |
| 41941.9462268519 | 181.2959193246 | 41941.9462268519 | |
| 42033.9462268519 | 183.8749718574 | 42033.9462268519 | |
| 42123.9462268519 | 186.4540243902 | 186.4540243902 | 42123.9462268519 |
| 42214.9462268519 | 189.0330769231 | 42214.9462268519 | |
| 42306.9462268519 | 191.6121294559 | 42306.9462268519 | |
| 42398.9462268519 | 194.1911819887 | 42398.9462268519 | |
| 42489.9462268519 | 196.7702345216 | 42489.9462268519 | |
| 42580.9462268519 | 199.3492870544 | 42580.9462268519 | |
| 42672.9462268519 | 201.9283395872 | 42672.9462268519 | |
| 42764.9462268519 | 204.5073921201 | 42764.9462268519 | |
| 42854.9462268519 | 207.0864446529 | 42854.9462268519 | |
| 42945.9462268519 | 209.6654971857 | 42945.9462268519 | |
| 43037.9462268519 | 212.2445497186 | 43037.9462268519 | |
| 43129.9462268519 | 214.8236022514 | 43129.9462268519 | |
| 43219.9462268519 | 217.4026547842 | 43219.9462268519 |
Actual
Forecast
Fitted Values
FURN ($Billions)
98.1
96.8
96
95
93.2
95.1
96.2
98.4
100.7
104.4
108.1
111.1
114.3
117.2
119.4
122.7
125.9
129.3
132.2
136.6
137.4
141.4
145.3
147.7
148.8
150.2
153.4
154.2
159.8
164.4
166.2
169.7
173.7
175.5
175
175.7
181.4
180
179.7
176.3
108
QS.11
QS.14
| State: Virginia |
| 1992 01 856414307. |
| 1993 01 216509630. |
| 1994 01 46593139. |
| 1995 01 566670693· |
| 1996 01 756750884. |
| 1997 01 806829183· |
| 1998 01 956900918. |
| 1999 01 447000174· |
| 2000 01 827105817. |
| 2001 01 447198362. |
| 2002 01 237286873· |
| 2003 01 707366977. |
| 2004 01 257475575· |
| 2005 01 617577105. |
| 2006 01 687673725· |
| 2007 01 487751000· |
| 2008 01 487833496. |
| 2009 01 87925937· |
| 2010 01 378025105. |
| 2011 01 158104384. |
| 2012 01 218185867. |
