Introduction

This exercise involves the development of a method to forecast future sales. There are two phases to this exercise; phase 1 develops a causal regression model while phase II develops an extrapolative model.

Fanfare International Inc. designs, distribute, and markets ceiling fans and lighting fixtures. The company's product line includes 120 basic models of ceiling fans and 138 compatible fan light kits and table lamps. In the summer of 1994, Fanfare decided it needed to develop forecasts of future sales to help determine future sales force needs, capital expenditures, and so on. The data file named FAN4 contains the following variables:

SALES = total monthly sales in thousands of dollars

ADEX = advertising expense in thousands of dollars

MTGRATE = mortgage rate for 30-year loans (%)

HSSTARTS = housing starts in thousands of units

The data are monthly and cover the period from July 1990 through May 1994.

As a consultant to Fanfare, your job is to find a causal regression model to forecast future sales.

First, make scatterplot showing sales on the Y-axis and Trend on the X-axis. Explain the how sales rose and fell over time.

Phase I. A causal regression model.

Perform a multiple regression relating Sales to ADEX, MTGRATE, and HSSTARTS.

Answer questions #1 - #5

Perform another multiple regression after removing any variable(s) that don't appear useful to the prediction of sales.

Answer questions #6 - #8

NOTE:

You should note that, to predict future sales, you would need to know future values of Mortgage rate, MTGRATE, and Housing starts, HSSTARTS which would be uncertain projections at best.

Phase II. An extrapolative regression model.

Perform a multiple regression relating Sales to Trend and LagSales.

Answer questions #9 - #11

1. What is the prediction equation for Sales, using all three predictor variables?

2. Now you will perform the "F-test for overall fit. Write out the Ho and Ha for this test for this dataset.

Ho:

Ha:

3. Check the p-value for the F statistic in the ANOVA table in order to perform the "F-test for overall fit. Compare this p-value to an alpha equal to 0.05. What decision to you make? Reject or not reject Ho?

4. What does your decision mean in everyday English?

5. Examine the p-values for each variable's coefficients. Compare these p-values with = 0.05. Do any variables appear to be not useful in the prediction of sales? If so, which one(s)? Use correlation matrix for independent variable to confirm your answer. You can use excel or R to do this.

Perform another multiple regression after removing any variable(s) that do not appear useful to the prediction of sales.

6. What is the prediction equation for Sales in this second analysis of Harris4?

7. Examine the p-values for each variable's coefficients. Compare these p-values with = 0.05. Do any variables appear to be not useful in the prediction of sales? If so, which ones?

8. Check out the Adjusted R² values for each of these two analyses. What are their values?

Adjusted R-Square for first analysis ____________________

Adjusted R-Square for second analysis _________________

NOTE:

Please note that, to predict future sales using model 1, you would need to know future values of Mortgage rate, MTGRATE, and Housing starts, HSSTARTS which would be uncertain projections at best. Now for phase II.

Now you will do Phase II of this exercise.

9. Are the Trend and One-period lag of sales useful as predictors? Check their p-values.

p-value for Trend _______________

p-value for one-period lag of sales __________________

What is the prediction equation for Sales in this lagged regression analysis?

10. Calculate a prediction of Sales for May of 1994. Show work for credit.

11. Check the rise and fall of sales in your scatterplot. Can you think of an equation that uses the trend, lag of sales, and one more variable that is not a lagged variable?