Question: The quarterly sales of a large manufacturer of spare parts

The quarterly sales of a large manufacturer of spare parts for automobiles are tabulated below. Since the sales are in millions of dollars, forecast errors can be costly. The company wants to forecast the sales as accurately as possible.
1. Carry out a Trend+Season forecast with the sales data, and forecast the sales for the four quarters of 2008. The director of marketing research of the company believes that the sales can be predicted better using a multiple regression of sales against three selected econometric variables that the director believes have significant impact on the sales. These variables are M2 Index, Non-Farm-Activity Index, and Oil Price. The values of these variables for the corresponding periods are available in the data tabulated to the left.
2. Conduct a multiple regression of sales against the three econometric variables, following the procedure learned in Chapter 11. What is the regression equation?
3. Make a prediction for the four quarters of 2008 based on the regression equation using projected values of the following econometric variables:
After seeing large errors and wide prediction intervals in the multiple regression approach to forecasting, the director of marketing research decides to include indicator variables to take into account the seasonal effects that may not be captured in the three independent variables. He adds the following three indicator variables:
He wants to run the multiple regression with a total of six independent variables—the original three plus the three indicator variables.
4. Carry out the multiple regression with the six independent variables and report the regression equation.
5. Make a forecast for the next four quarters with this new regression model.
6. Conduct a partial F test to test the claim that the three indicator variables can be dropped from the model.
7. Compare the forecasts from the three methods employed and rank order them according to their forecast accuracy.

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