Great Plains Roofing and Siding Company Inc. sells roofing and siding products to home repair retailers, such as Lowe’s and Home Depot, and commercial contractors. The owner is interested in studying the effects of several variables on the value of shingles sold ($000). The marketing manager is arguing that the company should spend more money on advertising, while a market researcher suggests it should focus more on making its brand and product more distinct from its competitors.

The company has divided the United States into 26 marketing districts. In each district, it collected information on the following variables: volume of sales (in thousands of dollars), advertising dollars (in thousands), number of active accounts, number of competing brands, and a rating of district 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 anyproblems?

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