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a. Develop a correlation matrix. Which independent variable has the strongest correla- tion 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?

a. Develop a correlation matrix. Which independent variable has the strongest correla- tion 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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 11CYU
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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: Cars Sold Last Month, Y 127 138 159 144 139 128 Advertising, X₁ 18 15 22 23 17 16 Sales Force, X₂ City, X₂ 10 Yes 15 No 14 Yes 12 Yes 12 12 No Yes Cars Sold Last Month, Y 161 180 102 163 106 149 Advertising, X₂ 25 26 15 24 18 25 Sales Force, x₂ 14 17 7 16 10 City, X3 Yes Yes No Yes No Yes a. Develop a correlation matrix. Which independent variable has the strongest correla- tion 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 net regression coefficients differ from zero. Let a = .05. d. Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Let a = .05.
Transcribed Image Text: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: Cars Sold Last Month, Y 127 138 159 144 139 128 Advertising, X₁ 18 15 22 23 17 16 Sales Force, X₂ City, X₂ 10 Yes 15 No 14 Yes 12 Yes 12 12 No Yes Cars Sold Last Month, Y 161 180 102 163 106 149 Advertising, X₂ 25 26 15 24 18 25 Sales Force, x₂ 14 17 7 16 10 City, X3 Yes Yes No Yes No Yes a. Develop a correlation matrix. Which independent variable has the strongest correla- tion 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 net regression coefficients differ from zero. Let a = .05. d. Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Let a = .05.
Correlations: Cars sold, Advertising, Sales Force, City Cars sold Advertising Sales Force -0.623 0.872 0.639 Advertising Sales Force City Cell Contents: Pearson correlation Predictor Constant Coef SE Coef 53.25 Advertising 0.6576 5.211 15.771 Regression Analysis: Cars sold versus Advertising, Sales Force, City The regression equation is Cars sold 53.2 + 0.658 Advertising + 5.21 Sales Force + 15.8 City = Sales Force City S = 8.84607 R-Sq 89.4% P T 12.13 4.39 0.4467 1.47 0.002 0.179 1.148 4.54 0.002 5.912 2.67 0.028 DE Analysis of Variance Source SS Regression 3 5298.6 Residual Error 8 626.0 Total 11 5924.7 0.517 0.281 Source DE Seq SS Advertising 1 2299.7 Sales Force 1 2442.0 City 1 556.9 R-Sq (adj) - 85.5% MS 1766.2 78.3 0.389 F 22.57 P 0.000
Transcribed Image Text:Correlations: Cars sold, Advertising, Sales Force, City Cars sold Advertising Sales Force -0.623 0.872 0.639 Advertising Sales Force City Cell Contents: Pearson correlation Predictor Constant Coef SE Coef 53.25 Advertising 0.6576 5.211 15.771 Regression Analysis: Cars sold versus Advertising, Sales Force, City The regression equation is Cars sold 53.2 + 0.658 Advertising + 5.21 Sales Force + 15.8 City = Sales Force City S = 8.84607 R-Sq 89.4% P T 12.13 4.39 0.4467 1.47 0.002 0.179 1.148 4.54 0.002 5.912 2.67 0.028 DE Analysis of Variance Source SS Regression 3 5298.6 Residual Error 8 626.0 Total 11 5924.7 0.517 0.281 Source DE Seq SS Advertising 1 2299.7 Sales Force 1 2442.0 City 1 556.9 R-Sq (adj) - 85.5% MS 1766.2 78.3 0.389 F 22.57 P 0.000
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