Great Plains Distributors Incorporated 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.


Sales (000s) Advertising Dollars (000s) Number of Accounts Number of Competitors Market Potential
79.3 5.5 31 10 8
200.1 2.5 55 8 6
163.2 8.0 67 12 9
200.1 3.0 50 7 16
146.0 3.0 38 8 15
177.7 2.9 71 12 17
30.9 8.0 30 12 8
291.9 9.0 56 5 10
160.0 4.0 42 8 4
339.4 6.5 73 5 16
159.6 5.5 60 11 7
86.3 5.0 44 12 12
237.5 6.0 50 6 6
107.2 5.0 39 10 4
155.0 3.5 55 10 4
291.4 8.0 70 6 14
100.2 6.0 40 11 6
135.8 4.0 50 11 8
223.3 7.5 62 9 13
195.0 7.0 59 9 11
73.4 6.7 53 13 5
47.7 6.1 38 13 10
140.7 3.6 43 9 17
93.5 4.2 26 8 3
259.0 4.5 75 8 19
331.2 5.6 71 4 9

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

4 scatter plots of sales versus advertising, accounts, competitors and potential. Scatterplot 1. The vertical axis plots sales ranging from 0 to 300 with increments of 100. The horizontal axis plots advertising ranging from 2 to 8 in increments of 2. The data is scattered over the whole range. Scatterplot 2. The vertical axis plots sales ranging from 0 to 300 with increments of 100. The horizontal axis plots accounts ranging from 30 to 70 in increments of 10. The data is scattered with an increasing trend. Scatterplot 3. The vertical axis plots sales ranging from 0 to 300 with increments of 100. The horizontal axis plots competitors ranging from 4 to 12 in increments of 2. The data is scattered with a decreasing tendency. Scatterplot 4. The vertical axis plots sales ranging from 0 to 300 with increments of 100. The horizontal axis plots potential ranging from 5 to 20 in increments of 5. The data is scattered over the whole range.


b-1. Compute a correlation matrix. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

b-3. Does it appear there are any redundant independent variables?




c-1. Perform a regression analysis using all independent variables and complete the following ANOVA table. (Leave no cells blank - be certain to enter "0" wherever required. Round your SS, MS values to whole number and F value to 2 decimal places.)



c-2. Find the standard error, R2 and R2(adjusted) values. (Round your answers to 1 decimal place.)




c-3. Using the regression analysis using all independent variables, complete the following table. (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by minus sign. Round your Coef, SE Coef, t to 2 decimal places and p-values to 3 decimal places.)

c-4. Using the regression analysis using all independent variables, complete the following multiple regression equation. (Negative amounts should be indicated by a minus sign. Round your constant value to a whole number and the rest of the values to 2 decimal places.)

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

e-1. Determine the regression equation by omitting the market potential variable. (Negative amounts should be indicated by a minus sign. Round the constant value to the nearest whole number and rest of the values to 2 decimal values.)



e-2. Using the regression analysis in e-1, complete the following table. (Negative amounts should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)



e-3. Determine the regression equation by omitting the advertising variable. (Negative amounts should be indicated by a minus sign. Round your constant value to the nearest whole number and the rest of the values to 2 decimal places.)



e-4. Using the regression analysis in e-3, complete the following table. (Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign. Round your Coef, SE Coef and t values to 2 decimal places.)

A histogram of the residuals (response is sales). The vertical axis plots frequency ranging from 0 to 9 in increments of 1 The horizontal axis plots residual value ranging from -20 to 20 in increments of 10. The values are as follow: (-20, 1), (-15, 2), (-10, 2), (5, 4), (0, 8), (5, 3), (10, 4), (15, 1), (20, 1). All values approximated.

The histogram appears to be normal.





g-1. Compute the variance inflation factor for the independent variables. (Round your answer to 1 decimal place.)

g-2. Does the variance inflation factor indicate the potential for any multicollinearity?