Ch.5 Appendix - Combination Models Exam Questions 7e - Forecasting with Forecast X 7e Complete Test Bank by Barry Keating. DOCX document preview.
Forecasting and Predictive Analytics with Forecast X, 7e (Keating)
Chapter 5 Appendix - Combination Models
1) Combining individual forecasts into one composite forecast is a way to
A) reduce forecast bias.
B) reduce autocorrelation.
C) enhance forecast optimality.
D) obtain forecast improvement.
E) All of the options are correct.
2) If you are restricted to using only one method to generate forecasts, you risk ignoring information regarding
A) a larger set of explanatory variables.
B) components of a data series emphasized by different models.
C) a larger set of relationships among variables.
D) the role of differing models' assumptions in the forecast process.
E) All of the options are correct.
3) The main purpose of combining forecasts is to reduce
A) bias.
B) mean forecasting bias.
C) mean squared forecasting error.
D) mean absolute forecasting error.
E) All of the options are correct.
4) Which of the following is not a source of forecast bias?
A) Omission of important variables
B) Incorrect model specification, i.e., linear vs. non-linear
C) The preconceived notions of the forecaster
D) Failure to account for serial correlation
E) All of the options are correct.
5) The methodology of combining forecasts is best described as
A) a moving average.
B) a simple average.
C) a geometric average.
D) a weighted average.
E) None of the options are correct.
6) In the optimal composite forecast process, which of the following is not true?
A) Use different models but the same data.
B) Use different models and different variables.
C) Use different data and different models.
D) Use different assumptions and different relationships.
E) All of the options are correct.
7) Which combination of forecasting models is likely to lead to the lowest RMSE of the combined forecast?
A) Trend regression and causal regression
B) Exponential smoothing and Holt's smoothing
C) Causal regression and ARIMA models
D) AR and MA models
E) None of the options are correct.
8) Which of the following is true about the convention, used by some, in which all forecasts are equally weighted in the composite process?
A) Such a weighting usually minimizes forecast error variance.
B) Such a weighting minimizes forecast bias.
C) Such a weighting minimizes RMSE.
D) Such a weighting removes any model bias on the part of the forecaster.
E) All of the options are correct.
9) Under what conditions will forecast combination not lead to increases in forecast accuracy?
A) If all models perform equally well
B) If the RMSE is the same across models
C) If the squared forecast errors are highly correlated across models
D) If all models use the same underlying data and assumptions
E) All of the options are correct.
10) If the squared forecast errors of two forecasting methods were perfectly negatively correlated, a composite forecast could be generated which would have a RMSE of
A) −1.
B) 0.
C) 1.
D) the model that performs the best.
E) None of the options are correct.
11) Which of the following is an advantage to using the adaptive approach to estimate the optimal weights in the forecast combination process?
A) The weights change from period to period.
B) A test of the combined forecast model bias can be performed.
C) The covariance between error variances is utilized.
D) Weights are chosen so as to maximize regression error variance.
E) All of the options are correct.
12) Which of the following is an advantage to using the regression approach to estimating the optimal weights in the forecast combination process?
A) The weights change from period to period.
B) A test of the combined forecast model bias can be performed.
C) The covariance between error variances is not utilized.
D) Weights are chosen so as to minimize absolute regression deviation.
E) All of the options are correct.
13) When using multiple regression to select the optimal weights for use in the composite forecast process, one can test whether forecast model 2 adds any explanatory power to what is already present in forecast model 1 using which distribution?
A) Chi-square
B) Standard normal
C) t distribution
D) F distribution
E) None of the options are correct.
14) Using the multiple regression approach to selecting optimal forecast combination weights, the null hypothesis of no composite model bias is
A) H0: s2 = 0.
B) H0: β1 = 0.
C) H0: β2 = 0.
D) H0: R2 = 0.
E) None of the options are correct.
15) Combination Forecast
Consider the ForecastX™ Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RFCST.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | −6,467.84 | 10,332.93 |
Gapsales_RFCST | Yes | 0.11 | 0.04 |
Gapsales_WFCST | Yes | 0.91 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | −0.63 | 0.39 | 5,005.67 | |
Gapsales_RFCST | 2.60 | 6.75 | 0.11 | |
Gapsales_WFCST | 22.58 | 510.08 | 0.90 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.38 |
| Durbin Watson | 1.75 |
|
BIC | 1,363.41 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.21 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 114,310,689,710.20 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,833.08 |
| Ljung-Box | 0.76 |
|
Mean Error | 0.00 |
|
|
|
|
Mean Square Error | 2,041,262,316.25 |
|
|
|
|
Root Mean Square Error | 45,180.33 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | 0.00 | 0.00 |
Gapsales_RFCST | Yes | 0.1018 | 0.04 |
Gapsales_WFCST | Yes | 0.9112 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | 0.00 | 0.00 | 5,062.49 | |
Gapsales_RFCST | 2.54 | 6.47 | 0.00 | |
Gapsales_WFCST | 22.70 | 515.50 | 0.91 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.80 |
| Durbin Watson | 1.72 |
|
BIC | 1,363.82 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.08 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 115,155,739,746 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,538.72 |
| Ljung-Box | 0.94 |
|
Mean Error | −2,333.11 |
|
|
|
|
Mean Square Error | 2,056,352,495.47 |
|
|
|
|
Root Mean Square Error | 45,347.02 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Forecast for 1999
Date | Gap Sales ($000) | Combined Forecast |
Mar-99 | 2277700 | 2,160,500.79 |
Jun-99 | 2453300 | 2,359,986.28 |
Sep-99 | 3045386 | 3,111,234.20 |
Dec-99 | 3858939 | 3,788,377.03 |
In the preparation of a combination forecast, Regression #1 above
A) is used to determine if there is no systematic bias in the two component models.
B) is used to determine if the two component models will contribute to the combined model.
C) is used to determine if each component model has an adequate t-statistic.
D) is used to determine if the Durbin Watson is close to 2.
16) Combination Forecast
Consider the ForecastX™ Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RFCST.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | −6,467.84 | 10,332.93 |
Gapsales_RFCST | Yes | 0.11 | 0.04 |
Gapsales_WFCST | Yes | 0.91 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | −0.63 | 0.39 | 5,005.67 | |
Gapsales_RFCST | 2.60 | 6.75 | 0.11 | |
Gapsales_WFCST | 22.58 | 510.08 | 0.90 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.38 |
| Durbin Watson | 1.75 |
|
BIC | 1,363.41 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.21 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 114,310,689,710.20 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,833.08 |
| Ljung-Box | 0.76 |
|
Mean Error | 0.00 |
|
|
|
|
Mean Square Error | 2,041,262,316.25 |
|
|
|
|
Root Mean Square Error | 45,180.33 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | 0.00 | 0.00 |
Gapsales_RFCST | Yes | 0.1018 | 0.04 |
Gapsales_WFCST | Yes | 0.9112 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | 0.00 | 0.00 | 5,062.49 | |
Gapsales_RFCST | 2.54 | 6.47 | 0.00 | |
Gapsales_WFCST | 22.70 | 515.50 | 0.91 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.80 |
| Durbin Watson | 1.72 |
|
BIC | 1,363.82 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.08 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 115,155,739,746 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,538.72 |
| Ljung-Box | 0.94 |
|
Mean Error | −2,333.11 |
|
|
|
|
Mean Square Error | 2,056,352,495.47 |
|
|
|
|
Root Mean Square Error | 45,347.02 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Forecast for 1999
Date | Gap Sales ($000) | Combined Forecast |
Mar-99 | 2277700 | 2,160,500.79 |
Jun-99 | 2453300 | 2,359,986.28 |
Sep-99 | 3045386 | 3,111,234.20 |
Dec-99 | 3858939 | 3,788,377.03 |
Regression #2 above is also used in the process of determining a combination model. Regression #2 above
A) can only be used if no bias exists in either candidate model.
B) is used to calculate the forecasts for the combined model.
C) is useful in determining the R2 of the combined model.
D) should have coefficients roughly summing to one.
E) All of the options are correct.
17) Combination Forecast
Consider the ForecastX™ Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RFCST.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | −6,467.84 | 10,332.93 |
Gapsales_RFCST | Yes | 0.11 | 0.04 |
Gapsales_WFCST | Yes | 0.91 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | −0.63 | 0.39 | 5,005.67 | |
Gapsales_RFCST | 2.60 | 6.75 | 0.11 | |
Gapsales_WFCST | 22.58 | 510.08 | 0.90 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.38 |
| Durbin Watson | 1.75 |
|
BIC | 1,363.41 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.21 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 114,310,689,710.20 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,833.08 |
| Ljung-Box | 0.76 |
|
Mean Error | 0.00 |
|
|
|
|
Mean Square Error | 2,041,262,316.25 |
|
|
|
|
Root Mean Square Error | 45,180.33 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | 0.00 | 0.00 |
Gapsales_RFCST | Yes | 0.1018 | 0.04 |
Gapsales_WFCST | Yes | 0.9112 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | 0.00 | 0.00 | 5,062.49 | |
Gapsales_RFCST | 2.54 | 6.47 | 0.00 | |
Gapsales_WFCST | 22.70 | 515.50 | 0.91 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.80 |
| Durbin Watson | 1.72 |
|
BIC | 1,363.82 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.08 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 115,155,739,746 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,538.72 |
| Ljung-Box | 0.94 |
|
Mean Error | −2,333.11 |
|
|
|
|
Mean Square Error | 2,056,352,495.47 |
|
|
|
|
Root Mean Square Error | 45,347.02 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Forecast for 1999
Date | Gap Sales ($000) | Combined Forecast |
Mar-99 | 2277700 | 2,160,500.79 |
Jun-99 | 2453300 | 2,359,986.28 |
Sep-99 | 3045386 | 3,111,234.20 |
Dec-99 | 3858939 | 3,788,377.03 |
The forecast for 1999 Gap Sales appearing above
A) was the result of an equal weight placed on each model.
B) was the result of applying the optimal weights to the two component forecasts.
C) was the result of Regression #1.
D) was not the result of using an optimal set of weights for the component models.
E) both "was the result of an equal weight placed on each model." and "was the result of applying the optimal weights to the two component forecasts." are correct.
18) Combination Forecast
Consider the ForecastX™ Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RFCST.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | −6,467.84 | 10,332.93 |
Gapsales_RFCST | Yes | 0.11 | 0.04 |
Gapsales_WFCST | Yes | 0.91 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | −0.63 | 0.39 | 5,005.67 | |
Gapsales_RFCST | 2.60 | 6.75 | 0.11 | |
Gapsales_WFCST | 22.58 | 510.08 | 0.90 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.38 |
| Durbin Watson | 1.75 |
|
BIC | 1,363.41 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.21 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 114,310,689,710.20 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,833.08 |
| Ljung-Box | 0.76 |
|
Mean Error | 0.00 |
|
|
|
|
Mean Square Error | 2,041,262,316.25 |
|
|
|
|
Root Mean Square Error | 45,180.33 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | 0.00 | 0.00 |
Gapsales_RFCST | Yes | 0.1018 | 0.04 |
Gapsales_WFCST | Yes | 0.9112 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | 0.00 | 0.00 | 5,062.49 | |
Gapsales_RFCST | 2.54 | 6.47 | 0.00 | |
Gapsales_WFCST | 22.70 | 515.50 | 0.91 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.80 |
| Durbin Watson | 1.72 |
|
BIC | 1,363.82 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.08 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 115,155,739,746 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,538.72 |
| Ljung-Box | 0.94 |
|
Mean Error | −2,333.11 |
|
|
|
|
Mean Square Error | 2,056,352,495.47 |
|
|
|
|
Root Mean Square Error | 45,347.02 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Forecast for 1999
Date | Gap Sales ($000) | Combined Forecast |
Mar-99 | 2277700 | 2,160,500.79 |
Jun-99 | 2453300 | 2,359,986.28 |
Sep-99 | 3045386 | 3,111,234.20 |
Dec-99 | 3858939 | 3,788,377.03 |
The optimal weights used in the 1999 forecast above
A) were about 0.51 for the regression model and 0.90 for the Winters model.
B) were about 0.1 for the regression model and 0.90 for the Winters model.
C) were about 0.0 for the regression model and 1.00 for the Winters model.
D) were about 1.00 for the regression model and 0.0 for the Winters model.
19) Combination Forecast
Consider the ForecastX™ Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RFCST.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | −6,467.84 | 10,332.93 |
Gapsales_RFCST | Yes | 0.11 | 0.04 |
Gapsales_WFCST | Yes | 0.91 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | −0.63 | 0.39 | 5,005.67 | |
Gapsales_RFCST | 2.60 | 6.75 | 0.11 | |
Gapsales_WFCST | 22.58 | 510.08 | 0.90 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.38 |
| Durbin Watson | 1.75 |
|
BIC | 1,363.41 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.21 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 114,310,689,710.20 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,833.08 |
| Ljung-Box | 0.76 |
|
Mean Error | 0.00 |
|
|
|
|
Mean Square Error | 2,041,262,316.25 |
|
|
|
|
Root Mean Square Error | 45,180.33 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Gap Sales ($000) | Dependent | 0.00 | 0.00 |
Gapsales_RFCST | Yes | 0.1018 | 0.04 |
Gapsales_WFCST | Yes | 0.9112 | 0.04 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
Gap Sales ($000) | 0.00 | 0.00 | 5,062.49 | |
Gapsales_RFCST | 2.54 | 6.47 | 0.00 | |
Gapsales_WFCST | 22.70 | 515.50 | 0.91 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 1,361.80 |
| Durbin Watson | 1.72 |
|
BIC | 1,363.82 |
| Mean | 804,816.13 |
|
Mean Absolute Percentage Error (MAPE) | 5.08 | % | Standard Deviation | 628,227.16 |
|
Sum Squared Error (SSE) | 115,155,739,746 |
| Max | 3,029,900.00 |
|
R-Square | 99.47 | % | Min | 105,715.00 |
|
Adjusted R-Square | 99.45 | % | Range | 2,924,185.00 |
|
Mean Absolute Error | 34,538.72 |
| Ljung-Box | 0.94 |
|
Mean Error | −2,333.11 |
|
|
|
|
Mean Square Error | 2,056,352,495.47 |
|
|
|
|
Root Mean Square Error | 45,347.02 |
|
|
|
|
Theil | 0.27 |
|
|
|
|
Forecast for 1999
Date | Gap Sales ($000) | Combined Forecast |
Mar-99 | 2277700 | 2,160,500.79 |
Jun-99 | 2453300 | 2,359,986.28 |
Sep-99 | 3045386 | 3,111,234.20 |
Dec-99 | 3858939 | 3,788,377.03 |
The constant term in Regression #2
A) does not exist.
B) is statistically insignificant.
C) equals 0.00.
D) determines the optimal weights for the combined model.
20) Combined Forecast #2
Consider the two regressions below that were used to determine the appropriateness of a combined model of Private Housing Starts. RFCST is the regression model of Private Housing Starts (PHS). WFCST is the Winters' exponential smoothing model of Private Housing Starts.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | −44.30 | 26.96 |
RFCST | Yes | 0.29 | 0.11 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | −1.64 | 2.70 | 226.75 | |
RFCST | 2.71 | 7.35 | 0.29 | |
WFCST | 18.71 | 350.24 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 281.49 |
| Durbin Watson | 2.21 |
| ||
BIC | 283.05 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.07 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6.020.44 |
| Max | 360.40 |
| ||
R-Square | 93.41 | % | Min | 146.70 |
| ||
Adjusted R-Square | 93.00 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.27 |
| Ljung-Box | 0.54 |
| ||
Mean Error | 0.00 |
|
|
|
| ||
Mean Square Error | 172.01 |
|
|
|
| ||
Root Mean Square Error | 13.12 |
|
|
|
| ||
Theil | 0.22 |
|
|
|
| ||
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | 0.00 | 0.00 |
RFCST | Yes | 0.13 | 0.05 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | 0.00 | 0.00 | 214.35 | |
RFCST | 2.70 | 7.29 | 0.00 | |
WFCST | 18.18 | 330.49 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 284.33 |
| Durbin Watson | 1.99 |
| ||
BIC | 285.88 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.34 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6,528.68 |
| Max | 360.40 |
| ||
R-Square | 92.85 | % | Min | 146.70 |
| ||
Adjusted R-Square | 92.41 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.91 |
| Ljung-Box | 0.00 |
| ||
Mean Error | −0.33 |
|
|
|
| ||
Mean Square Error | 186.53 |
|
|
|
| ||
Root Mean Square Error | 13.66 |
|
|
|
| ||
Theil | 0.23 |
|
|
|
| ||
Regression #1 above is used
A) to determine if the component models are sufficiently unbiased.
B) to determine if both component models are statistically significant.
C) to determine if the component models suffer from autocorrelation.
D) to determine how to weight the component models.
21) Combined Forecast #2
Consider the two regressions below that were used to determine the appropriateness of a combined model of Private Housing Starts. RFCST is the regression model of Private Housing Starts (PHS). WFCST is the Winters' exponential smoothing model of Private Housing Starts.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | −44.30 | 26.96 |
RFCST | Yes | 0.29 | 0.11 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | −1.64 | 2.70 | 226.75 | |
RFCST | 2.71 | 7.35 | 0.29 | |
WFCST | 18.71 | 350.24 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 281.49 |
| Durbin Watson | 2.21 |
| ||
BIC | 283.05 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.07 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6.020.44 |
| Max | 360.40 |
| ||
R-Square | 93.41 | % | Min | 146.70 |
| ||
Adjusted R-Square | 93.00 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.27 |
| Ljung-Box | 0.54 |
| ||
Mean Error | 0.00 |
|
|
|
| ||
Mean Square Error | 172.01 |
|
|
|
| ||
Root Mean Square Error | 13.12 |
|
|
|
| ||
Theil | 0.22 |
|
|
|
| ||
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | 0.00 | 0.00 |
RFCST | Yes | 0.13 | 0.05 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | 0.00 | 0.00 | 214.35 | |
RFCST | 2.70 | 7.29 | 0.00 | |
WFCST | 18.18 | 330.49 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 284.33 |
| Durbin Watson | 1.99 |
| ||
BIC | 285.88 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.34 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6,528.68 |
| Max | 360.40 |
| ||
R-Square | 92.85 | % | Min | 146.70 |
| ||
Adjusted R-Square | 92.41 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.91 |
| Ljung-Box | 0.00 |
| ||
Mean Error | −0.33 |
|
|
|
| ||
Mean Square Error | 186.53 |
|
|
|
| ||
Root Mean Square Error | 13.66 |
|
|
|
| ||
Theil | 0.23 |
|
|
|
| ||
Regression #2 above is used
A) to ensure that the combined model is unbiased.
B) to calculate the weights of the combined model.
C) to eliminate autocorrelation in the combined model.
D) to determine the correlation between the component models.
22) Combined Forecast #2
Consider the two regressions below that were used to determine the appropriateness of a combined model of Private Housing Starts. RFCST is the regression model of Private Housing Starts (PHS). WFCST is the Winters' exponential smoothing model of Private Housing Starts.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | −44.30 | 26.96 |
RFCST | Yes | 0.29 | 0.11 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | −1.64 | 2.70 | 226.75 | |
RFCST | 2.71 | 7.35 | 0.29 | |
WFCST | 18.71 | 350.24 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 281.49 |
| Durbin Watson | 2.21 |
| ||
BIC | 283.05 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.07 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6.020.44 |
| Max | 360.40 |
| ||
R-Square | 93.41 | % | Min | 146.70 |
| ||
Adjusted R-Square | 93.00 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.27 |
| Ljung-Box | 0.54 |
| ||
Mean Error | 0.00 |
|
|
|
| ||
Mean Square Error | 172.01 |
|
|
|
| ||
Root Mean Square Error | 13.12 |
|
|
|
| ||
Theil | 0.22 |
|
|
|
| ||
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | 0.00 | 0.00 |
RFCST | Yes | 0.13 | 0.05 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | 0.00 | 0.00 | 214.35 | |
RFCST | 2.70 | 7.29 | 0.00 | |
WFCST | 18.18 | 330.49 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 284.33 |
| Durbin Watson | 1.99 |
| ||
BIC | 285.88 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.34 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6,528.68 |
| Max | 360.40 |
| ||
R-Square | 92.85 | % | Min | 146.70 |
| ||
Adjusted R-Square | 92.41 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.91 |
| Ljung-Box | 0.00 |
| ||
Mean Error | −0.33 |
|
|
|
| ||
Mean Square Error | 186.53 |
|
|
|
| ||
Root Mean Square Error | 13.66 |
|
|
|
| ||
Theil | 0.23 |
|
|
|
| ||
The two regressions above show
A) that there would be little advantage to combining these two models.
B) that the models should be weighted approximately 0.13 for the regression model and 0.88 for the Winters' model.
C) that the appropriate weighting is about 0.88 for the regression model and about 0.13 for the Winters' model.
D) that an even weighting (i.e., 0.50 for each model) would be appropriate.
23) Combined Forecast #2
Consider the two regressions below that were used to determine the appropriateness of a combined model of Private Housing Starts. RFCST is the regression model of Private Housing Starts (PHS). WFCST is the Winters' exponential smoothing model of Private Housing Starts.
Regression #1
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | −44.30 | 26.96 |
RFCST | Yes | 0.29 | 0.11 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | −1.64 | 2.70 | 226.75 | |
RFCST | 2.71 | 7.35 | 0.29 | |
WFCST | 18.71 | 350.24 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 281.49 |
| Durbin Watson | 2.21 |
| ||
BIC | 283.05 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.07 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6.020.44 |
| Max | 360.40 |
| ||
R-Square | 93.41 | % | Min | 146.70 |
| ||
Adjusted R-Square | 93.00 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.27 |
| Ljung-Box | 0.54 |
| ||
Mean Error | 0.00 |
|
|
|
| ||
Mean Square Error | 172.01 |
|
|
|
| ||
Root Mean Square Error | 13.12 |
|
|
|
| ||
Theil | 0.22 |
|
|
|
| ||
Regression #2
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
PHS | Dependent | 0.00 | 0.00 |
RFCST | Yes | 0.13 | 0.05 |
WFCST | Yes | 0.88 | 0.05 |
Series Description | T-test | F-test | Elasticity | Overall F-test |
PHS | 0.00 | 0.00 | 214.35 | |
RFCST | 2.70 | 7.29 | 0.00 | |
WFCST | 18.18 | 330.49 | 0.88 |
Audit Trail - Statistics |
| ||||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| ||
AIC | 284.33 |
| Durbin Watson | 1.99 |
| ||
BIC | 285.88 |
| Mean | 271.85 |
| ||
Mean Absolute Percentage Error (MAPE) | 4.34 | % | Standard Deviation | 51.83 |
| ||
Sum Squared Error (SSE) | 6,528.68 |
| Max | 360.40 |
| ||
R-Square | 92.85 | % | Min | 146.70 |
| ||
Adjusted R-Square | 92.41 | % | Range | 213.70 |
| ||
Mean Absolute Error | 10.91 |
| Ljung-Box | 0.00 |
| ||
Mean Error | −0.33 |
|
|
|
| ||
Mean Square Error | 186.53 |
|
|
|
| ||
Root Mean Square Error | 13.66 |
|
|
|
| ||
Theil | 0.23 |
|
|
|
| ||
The two regressions above
A) show significant bias in one or more of the two models.
B) show little bias in either model.
C) fail to determine if there is any bias in either of the models.
D) None of the options are correct.
24) Combined Forecast #3
Consider the data below that includes a time series of shipments of a commercial product. Two separate forecasts models were estimated for this data; one is a Holt-Winter's model labeled "winters" and the other is a sales-force composite judgmental model labeled "purchaser's survey."
Date | Shipments | Winters | Purchaser's Survey |
Apr-2002 | 13,838.00 | 12,867.74 | 13,920.32 |
May-2002 | 15,137.00 | 15,020.45 | 15,052.82 |
Jun-2002 | 23,713.00 | 20,396.51 | 26,207.69 |
Jul-2002 | 17,141.00 | 13,705.67 | 17,237.59 |
Aug-2002 | 7,107.00 | 7,973.83 | 7,687.23 |
Sep-2002 | 9,225.00 | 10,588.46 | 9,788.06 |
Oct-2002 | 10,950.00 | 13,110.02 | 7,889.46 |
Nov-2002 | 14,752.00 | 14,920.97 | 14,679.10 |
Dec-2002 | 18,871.00 | 21,429.51 | 17,644.48 |
Jan-2003 | 11,329.00 | 14,836.31 | 10,436.45 |
Feb-2003 | 6,555.00 | 7,561.41 | 6,304.89 |
Mar-2003 | 9,335.00 | 9,956.32 | 9,354.44 |
Apr-2003 | 10,845.00 | 12,148.06 | 11,759.15 |
May-2003 | 15,185.00 | 14,665.88 | 14,971.57 |
Jun-2003 | 21,056.00 | 20,200.90 | 24,644.20 |
Jul-2003 | 13,509.00 | 13,344.02 | 14,224.17 |
Aug-2003 | 9,729.00 | 7,090.84 | 9,194.77 |
Sep-2003 | 13,454.00 | 9,606.14 | 12,141.25 |
Oct-2003 | 13,426.00 | 11,533.95 | 11,971.93 |
Nov-2003 | 17,792.00 | 14,714.76 | 17,654.14 |
Dec-2003 | 19,026.00 | 20,342.11 | 15,580.19 |
Jan-2004 | 9,432.00 | 13,296.42 | 9,961.98 |
Feb-2004 | 6,356.00 | 8,010.78 | 7,368.55 |
Mar-2004 | 12,893.00 | 10,944.75 | 11,286.25 |
Apr-2004 | 19,379.00 | 12,126.72 | 18,915.33 |
May-2004 | 14,542.00 | 15,732.13 | 14,056.06 |
Jun-2004 | 18,043.00 | 19,676.43 | 20,699.38 |
Jul-2004 | 10,803.00 | 11,747.86 | 12,892.97 |
Regression #1
Audit Trail — ANOVA Table (Multiple Regression Selected) | ||||||||||||||||
Source of Variation | SS | df | MS | SEE | ||||||||||||
Regression |
| 502,795,011.49 |
|
| 2 |
|
| 251,397,505.75 |
|
|
|
| ||||
Error |
| 44,550,454.61 |
|
| 25 |
|
| 1,782,018.18 |
|
| 1,334.92 |
| ||||
Total |
| 547,345,466.11 |
|
| 27 |
|
|
|
|
|
|
| ||||
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Shipments | Dependent | 875.23 | 890.48 |
Winters | Yes | 0.22 | 0.11 |
Purchaser's Survey | Yes | 0.72 | 0.09 |
Series Description | T-test | P-value | F-test | Elasticity | Overall F-test |
Shipments | 0.98 | 0.34 | 0.97 | 141.07 | |
Winters | 2.09 | 0.05 | 4.35 | 0.22 | |
Purchaser's Survey | 8.25 | 0.00 | 68.11 | 0.72 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 481.30 |
| Durbin Watson(1) | 1.48 |
|
BIC | 482.63 |
| Mean | 13,693.68 |
|
Mean Absolute Percentage Error (MAPE) | 8.45 | % | Max | 23,713.00 |
|
R-Square | 91.86 | % | Min | 6,356.00 |
|
Adjusted R-Square | 91.21 | % | Sum Squared Deviation | 547,345,466.11 |
|
Root Mean Square Error | 1,261.38 |
| Range | 17,357.00 |
|
Theil | 0.27 |
| Ljung-Box | 9.64 |
|
|
|
|
|
|
|
Method Statistics | Value |
|
|
|
|
Method Selected | Multiple Regression |
|
|
|
|
Regression #2
Audit Trail — ANOVA Table (Multiple Regression Selected) | ||||||||||||||||
Source of Variation | SS | df | MS | SEE | ||||||||||||
Regression |
| 501,073,510.18 |
|
| 2 |
|
| 250,536,755.09 |
|
|
|
| ||||
Error |
| 46,271,955.92 |
|
| 26 |
|
| 1,779,690.61 |
|
| 1,334.05 |
| ||||
Total |
| 547,345,466.11 |
|
| 28 |
|
|
|
|
|
|
| ||||
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Shipments | Dependent | 0.00 | 0.00 |
Winters | Yes | 0.28 | 0.09 |
Purchaser's Survey | Yes | 0.72 | 0.09 |
Series Description | T-test | P-value | F-test | Elasticity | Overall F-test |
Shipments | 0.00 | 0.00 | 0.00 | 140.78 | |
Winters | 3.09 | 0.00 | 9.54 | 0.27 | |
Purchaser's Survey | 8.31 | 0.00 | 69.09 | 0.72 |
Audit Trail - Statistics |
| |||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| |
AIC | 482.36 |
| Durbin Watson(1) | 1.44 |
| |
BIC | 483.69 |
| Mean | 13,693.68 |
| |
Mean Absolute Percentage Error (MAPE) | 7.89 | % | Max | 23,713.00 |
| |
R-Square | 91.55 | % | Min | 6,356.00 |
| |
Adjusted R-Square | 90.87 | % | Sum Squared Deviation | 547,345,466.11 |
| |
Root Mean Square Error | 1,285.52 |
| Range | 17,357.00 |
| |
Theil | 0.28 |
| Ljung-Box | 11.58 |
| |
|
|
|
|
|
| |
Method Statistics | Value |
|
|
|
| |
Method Selected | Multiple Regression |
|
|
|
| |
Both models were used in a regression model labeled "regression #1" above to examine the portfolio of forecasts. Is there evidence of bias in the combined forecast?
A) Yes.
B) No.
C) This is the wrong regression model to use for bias determination.
D) Bias must be measured using correlation analysis.
25) Combined Forecast #3
Consider the data below that includes a time series of shipments of a commercial product. Two separate forecasts models were estimated for this data; one is a Holt-Winter's model labeled "winters" and the other is a sales-force composite judgmental model labeled "purchaser's survey."
Date | Shipments | Winters | Purchaser's Survey |
Apr-2002 | 13,838.00 | 12,867.74 | 13,920.32 |
May-2002 | 15,137.00 | 15,020.45 | 15,052.82 |
Jun-2002 | 23,713.00 | 20,396.51 | 26,207.69 |
Jul-2002 | 17,141.00 | 13,705.67 | 17,237.59 |
Aug-2002 | 7,107.00 | 7,973.83 | 7,687.23 |
Sep-2002 | 9,225.00 | 10,588.46 | 9,788.06 |
Oct-2002 | 10,950.00 | 13,110.02 | 7,889.46 |
Nov-2002 | 14,752.00 | 14,920.97 | 14,679.10 |
Dec-2002 | 18,871.00 | 21,429.51 | 17,644.48 |
Jan-2003 | 11,329.00 | 14,836.31 | 10,436.45 |
Feb-2003 | 6,555.00 | 7,561.41 | 6,304.89 |
Mar-2003 | 9,335.00 | 9,956.32 | 9,354.44 |
Apr-2003 | 10,845.00 | 12,148.06 | 11,759.15 |
May-2003 | 15,185.00 | 14,665.88 | 14,971.57 |
Jun-2003 | 21,056.00 | 20,200.90 | 24,644.20 |
Jul-2003 | 13,509.00 | 13,344.02 | 14,224.17 |
Aug-2003 | 9,729.00 | 7,090.84 | 9,194.77 |
Sep-2003 | 13,454.00 | 9,606.14 | 12,141.25 |
Oct-2003 | 13,426.00 | 11,533.95 | 11,971.93 |
Nov-2003 | 17,792.00 | 14,714.76 | 17,654.14 |
Dec-2003 | 19,026.00 | 20,342.11 | 15,580.19 |
Jan-2004 | 9,432.00 | 13,296.42 | 9,961.98 |
Feb-2004 | 6,356.00 | 8,010.78 | 7,368.55 |
Mar-2004 | 12,893.00 | 10,944.75 | 11,286.25 |
Apr-2004 | 19,379.00 | 12,126.72 | 18,915.33 |
May-2004 | 14,542.00 | 15,732.13 | 14,056.06 |
Jun-2004 | 18,043.00 | 19,676.43 | 20,699.38 |
Jul-2004 | 10,803.00 | 11,747.86 | 12,892.97 |
Regression #1
Audit Trail — ANOVA Table (Multiple Regression Selected) | ||||||||||||||||
Source of Variation | SS | df | MS | SEE | ||||||||||||
Regression |
| 502,795,011.49 |
|
| 2 |
|
| 251,397,505.75 |
|
|
|
| ||||
Error |
| 44,550,454.61 |
|
| 25 |
|
| 1,782,018.18 |
|
| 1,334.92 |
| ||||
Total |
| 547,345,466.11 |
|
| 27 |
|
|
|
|
|
|
| ||||
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Shipments | Dependent | 875.23 | 890.48 |
Winters | Yes | 0.22 | 0.11 |
Purchaser's Survey | Yes | 0.72 | 0.09 |
Series Description | T-test | P-value | F-test | Elasticity | Overall F-test |
Shipments | 0.98 | 0.34 | 0.97 | 141.07 | |
Winters | 2.09 | 0.05 | 4.35 | 0.22 | |
Purchaser's Survey | 8.25 | 0.00 | 68.11 | 0.72 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 481.30 |
| Durbin Watson(1) | 1.48 |
|
BIC | 482.63 |
| Mean | 13,693.68 |
|
Mean Absolute Percentage Error (MAPE) | 8.45 | % | Max | 23,713.00 |
|
R-Square | 91.86 | % | Min | 6,356.00 |
|
Adjusted R-Square | 91.21 | % | Sum Squared Deviation | 547,345,466.11 |
|
Root Mean Square Error | 1,261.38 |
| Range | 17,357.00 |
|
Theil | 0.27 |
| Ljung-Box | 9.64 |
|
|
|
|
|
|
|
Method Statistics | Value |
|
|
|
|
Method Selected | Multiple Regression |
|
|
|
|
Regression #2
Audit Trail — ANOVA Table (Multiple Regression Selected) | ||||||||||||||||
Source of Variation | SS | df | MS | SEE | ||||||||||||
Regression |
| 501,073,510.18 |
|
| 2 |
|
| 250,536,755.09 |
|
|
|
| ||||
Error |
| 46,271,955.92 |
|
| 26 |
|
| 1,779,690.61 |
|
| 1,334.05 |
| ||||
Total |
| 547,345,466.11 |
|
| 28 |
|
|
|
|
|
|
| ||||
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Shipments | Dependent | 0.00 | 0.00 |
Winters | Yes | 0.28 | 0.09 |
Purchaser's Survey | Yes | 0.72 | 0.09 |
Series Description | T-test | P-value | F-test | Elasticity | Overall F-test |
Shipments | 0.00 | 0.00 | 0.00 | 140.78 | |
Winters | 3.09 | 0.00 | 9.54 | 0.27 | |
Purchaser's Survey | 8.31 | 0.00 | 69.09 | 0.72 |
Audit Trail - Statistics |
| |||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| |
AIC | 482.36 |
| Durbin Watson(1) | 1.44 |
| |
BIC | 483.69 |
| Mean | 13,693.68 |
| |
Mean Absolute Percentage Error (MAPE) | 7.89 | % | Max | 23,713.00 |
| |
R-Square | 91.55 | % | Min | 6,356.00 |
| |
Adjusted R-Square | 90.87 | % | Sum Squared Deviation | 547,345,466.11 |
| |
Root Mean Square Error | 1,285.52 |
| Range | 17,357.00 |
| |
Theil | 0.28 |
| Ljung-Box | 11.58 |
| |
|
|
|
|
|
| |
Method Statistics | Value |
|
|
|
| |
Method Selected | Multiple Regression |
|
|
|
| |
For the "shipments" data above the RMSE of the sales-force composite forecast was 1520 and for the Winters model the RMSE was 2461. Considering this piece of information, if you are determined to minimize historical forecast error, what model would you choose?
A) The sales-force composite model
B) The Winters model
C) The combined model
D) Unable to answer from data provided
26) Combined Forecast #3
Consider the data below that includes a time series of shipments of a commercial product. Two separate forecasts models were estimated for this data; one is a Holt-Winter's model labeled "winters" and the other is a sales-force composite judgmental model labeled "purchaser's survey."
Date | Shipments | Winters | Purchaser's Survey |
Apr-2002 | 13,838.00 | 12,867.74 | 13,920.32 |
May-2002 | 15,137.00 | 15,020.45 | 15,052.82 |
Jun-2002 | 23,713.00 | 20,396.51 | 26,207.69 |
Jul-2002 | 17,141.00 | 13,705.67 | 17,237.59 |
Aug-2002 | 7,107.00 | 7,973.83 | 7,687.23 |
Sep-2002 | 9,225.00 | 10,588.46 | 9,788.06 |
Oct-2002 | 10,950.00 | 13,110.02 | 7,889.46 |
Nov-2002 | 14,752.00 | 14,920.97 | 14,679.10 |
Dec-2002 | 18,871.00 | 21,429.51 | 17,644.48 |
Jan-2003 | 11,329.00 | 14,836.31 | 10,436.45 |
Feb-2003 | 6,555.00 | 7,561.41 | 6,304.89 |
Mar-2003 | 9,335.00 | 9,956.32 | 9,354.44 |
Apr-2003 | 10,845.00 | 12,148.06 | 11,759.15 |
May-2003 | 15,185.00 | 14,665.88 | 14,971.57 |
Jun-2003 | 21,056.00 | 20,200.90 | 24,644.20 |
Jul-2003 | 13,509.00 | 13,344.02 | 14,224.17 |
Aug-2003 | 9,729.00 | 7,090.84 | 9,194.77 |
Sep-2003 | 13,454.00 | 9,606.14 | 12,141.25 |
Oct-2003 | 13,426.00 | 11,533.95 | 11,971.93 |
Nov-2003 | 17,792.00 | 14,714.76 | 17,654.14 |
Dec-2003 | 19,026.00 | 20,342.11 | 15,580.19 |
Jan-2004 | 9,432.00 | 13,296.42 | 9,961.98 |
Feb-2004 | 6,356.00 | 8,010.78 | 7,368.55 |
Mar-2004 | 12,893.00 | 10,944.75 | 11,286.25 |
Apr-2004 | 19,379.00 | 12,126.72 | 18,915.33 |
May-2004 | 14,542.00 | 15,732.13 | 14,056.06 |
Jun-2004 | 18,043.00 | 19,676.43 | 20,699.38 |
Jul-2004 | 10,803.00 | 11,747.86 | 12,892.97 |
Regression #1
Audit Trail — ANOVA Table (Multiple Regression Selected) | ||||||||||||||||
Source of Variation | SS | df | MS | SEE | ||||||||||||
Regression |
| 502,795,011.49 |
|
| 2 |
|
| 251,397,505.75 |
|
|
|
| ||||
Error |
| 44,550,454.61 |
|
| 25 |
|
| 1,782,018.18 |
|
| 1,334.92 |
| ||||
Total |
| 547,345,466.11 |
|
| 27 |
|
|
|
|
|
|
| ||||
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Shipments | Dependent | 875.23 | 890.48 |
Winters | Yes | 0.22 | 0.11 |
Purchaser's Survey | Yes | 0.72 | 0.09 |
Series Description | T-test | P-value | F-test | Elasticity | Overall F-test |
Shipments | 0.98 | 0.34 | 0.97 | 141.07 | |
Winters | 2.09 | 0.05 | 4.35 | 0.22 | |
Purchaser's Survey | 8.25 | 0.00 | 68.11 | 0.72 |
Audit Trail - Statistics |
| ||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
|
AIC | 481.30 |
| Durbin Watson(1) | 1.48 |
|
BIC | 482.63 |
| Mean | 13,693.68 |
|
Mean Absolute Percentage Error (MAPE) | 8.45 | % | Max | 23,713.00 |
|
R-Square | 91.86 | % | Min | 6,356.00 |
|
Adjusted R-Square | 91.21 | % | Sum Squared Deviation | 547,345,466.11 |
|
Root Mean Square Error | 1,261.38 |
| Range | 17,357.00 |
|
Theil | 0.27 |
| Ljung-Box | 9.64 |
|
|
|
|
|
|
|
Method Statistics | Value |
|
|
|
|
Method Selected | Multiple Regression |
|
|
|
|
Regression #2
Audit Trail — ANOVA Table (Multiple Regression Selected) | ||||||||||||||||
Source of Variation | SS | df | MS | SEE | ||||||||||||
Regression |
| 501,073,510.18 |
|
| 2 |
|
| 250,536,755.09 |
|
|
|
| ||||
Error |
| 46,271,955.92 |
|
| 26 |
|
| 1,779,690.61 |
|
| 1,334.05 |
| ||||
Total |
| 547,345,466.11 |
|
| 28 |
|
|
|
|
|
|
| ||||
Audit Trail — Coefficient Table (Multiple Regression Selected)
Series Description | Included in Model | Coefficient | Standard Error |
Shipments | Dependent | 0.00 | 0.00 |
Winters | Yes | 0.28 | 0.09 |
Purchaser's Survey | Yes | 0.72 | 0.09 |
Series Description | T-test | P-value | F-test | Elasticity | Overall F-test |
Shipments | 0.00 | 0.00 | 0.00 | 140.78 | |
Winters | 3.09 | 0.00 | 9.54 | 0.27 | |
Purchaser's Survey | 8.31 | 0.00 | 69.09 | 0.72 |
Audit Trail - Statistics |
| |||||
Accuracy Measures | Value |
| Forecast Statistics | Value |
| |
AIC | 482.36 |
| Durbin Watson(1) | 1.44 |
| |
BIC | 483.69 |
| Mean | 13,693.68 |
| |
Mean Absolute Percentage Error (MAPE) | 7.89 | % | Max | 23,713.00 |
| |
R-Square | 91.55 | % | Min | 6,356.00 |
| |
Adjusted R-Square | 90.87 | % | Sum Squared Deviation | 547,345,466.11 |
| |
Root Mean Square Error | 1,285.52 |
| Range | 17,357.00 |
| |
Theil | 0.28 |
| Ljung-Box | 11.58 |
| |
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|
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Method Statistics | Value |
|
|
|
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Method Selected | Multiple Regression |
|
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The information represented above for "shipments" "regression #2"
A) is used to determine bias.
B) is used to determine the appropriateness of combining the two separate models.
C) does not pass the Ljung-Box test.
D) suggests that an unequal weighting of the models could be optimal.
27) Suppose you are given 'n' predictions on test data by 'n' different models (M1, M2, …. Mn) respectively. Which of the following methods can be used to combine the predictions of these models?
1. Median
2. Product
3. Average
4. Weighted sum
5. Minimum and Maximum
6. Regression optimized weighting
A) 1, 3, and 4
B) 1, 3, and 6
C) 1, 3, 4, and 6
D) All of the options are correct.
28) How can we assign the weights to output of different models in an ensemble?
1. Use an algorithm to return the optimal weights
2. Choose the weights using cross validation
3. Give high weights to more accurate models
A) 1 and 2
B) 1 and 3
C) 2 and 3
D) All of the options are correct.
Document Information
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