Great Plains Distributors Inc. sells roofing and siding products to home improvement retailers, such as Lowe’s and Home Depot, and commercial contractors. The owner is interested in studying the effects of several variables on the sales volume of fiber-cement siding products. The company has 26 marketing districts across the United States. In each district, it collected information on the following variables: sales volume (in thousands of dollars), advertising dollars (in thousands), number of active accounts, number of competing brands, and a rating of market potential.

Conduct a multiple regression analysis to find the best predictors of sales.

a. Draw a scatter diagram comparing sales volume with each of the independent variables. Comment on the results.

b. Develop a correlation matrix. Do you see any problems? Does it appear there are any redundant independent variables?

c. Develop a regression equation. Conduct the global test. Can we conclude that some of the independent variables are useful in explaining the variation in the dependent variable?

d. Conduct a test of each of the independent variables. Are there any that should be dropped?

e. Refine the regression equation so the remaining variables are all significant.

f. Develop a histogram of the residuals and a normal probability plot. Are there any problems?

g. Determine the variance inflation factor for each of the independent variables. Are there any problems?

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Advertising Sales Dollars Number of Number of Market (000s) (000s) Accounts Competitors Potential 79.3 5.5 31 10 8 200.1 2.5 55 8 163.2 8.0 67 12 200.1 3.0 50 7 16 146.0 3.0 38 8 15 177.7 2.9 71 17 93.5 4.2 26 8 3 259.0 4.5 75 8 19 331.2 5.6 71 4 12