The district sales manager for a major automobile manufacturer is studying car sales. Specifically, he would like to determine what factors affect the number of cars sold at a dealership. To investigate, he randomly selects 12 dealers. From these dealers he obtains the number of cars sold last month, the minutes of radio advertising purchased last month, the number of full-time salespeople employed in the dealership, and whether the dealer is located in the city. The information is as follows:

a. Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable? Does it appear there will be any problems with multicollinearity?

b. Determine the regression equation. How many cars would you expect to be sold by a dealership employing 20 salespeople, purchasing 15 minutes of advertising, and located in a city?

c. Conduct a global test of hypothesis to determine whether any of the regression coefficients differ from zero. Let α = .05.

d. Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Let α = .05.

e. If your conclusion in part

(d) was to delete one or more independent variables, run the analysis again without those variables.

f. Determine the residuals for the equation of part (e). Use a stem-andleaf chart or a histogram to verify that the distribution of the residuals is approximately normal.
g. Plot the residuals computed in part

(f) in a scatter diagram with the residuals on the Y-axis and the Ŷ values on the X-axis. Does the plot reveal any violations of the assumptions of regression?

Transcribed Image Text:

Cars Sold Last Month, Sales Cars Sold Sales Advertising, Force, City, Last Month, Advertising, Force, City, Y X X2 X Y Y X X2 X 127 18 138 15 159 22 154 10 Yes 161 25 14 Yes No 180 26 17 Yes Yes 102 15 7 No 144 23 12 Yes 163 24 16 Yes 139 17 12 No 106 18 10 No 128 16 12 Yes 149 25 11 Yes