The sales manager of a large automotive parts distributor wants to estimate the total annual sales for each of the company's regions. Five factors appear to be related to regional sales: the number of retail outlets in the region, the number of automobiles in the region registered as of April 1, the total personal income recorded in the first quarter of the year, the average age of the automobiles (years). and the number of sales supervisors in the region. The data for each region were gathered for last year. For example, see the following table. In region 1 there were 1,739 retail outlets stocking the company's automotive parts, there were 9.270,000 registered automobiles in the region as of April 1. and so on. The region's sales for that year were $37,702,000. Number of Annual Sales ($ Number of Automobiles Personal Income Average Age of Number of millions) , Retail Outlets, Registered ($ billions) , Automobiles Supervisors, *1 (millions ), *2 X3 (years ) , x4 X'S 37.702 1,739 9.27 85.4 3.5 24. 196 1, 221 5.86 69.7 5.6 5.8 32.055 1, 846 8. 81 68.1 4.4 7.8 3. 611 128 3.81 20.2 4.0 5.0 17. 625 1, 896 10. 31 33.8 3.5 7.8 45.919 2,298 11. 62 95. 1 4.1 13.0 29. 689 1, 687 8.96 69.3 4.1 15.8 8. 114 241 6.28 16.3 5.9 11.0 20. 116 649 7.77 34.9 5.5 16. 0 12.994 1, 427 19.92 15.1 4.1 10.8 a. Consider the following correlation matrix. Which single variable has the strongest correlation with the dependent variable? The correlations between the independent variables outlets and income and between outlets and number of automobiles are fairly strong. Could this be a problem? What is this condition called? sales outlets cars income age outlets 9. 899 automobiles 9. 605 0.775 income 9.964 0.825 8. 489 age -0.323 -0.489 -0. 447 -0.349 bosses 9. 286 0.183 0. 395 0. 155 0.291 The strongest relationship is between A problem if both "cars" and "outlets" are part of the final solution. Also, outlets and income are strongly correlated. This is calledb. The following regression equation was obtained using the five independent variables. What percent of the variation is explained by the regression equation? (Round your answer to 4 decimal places.) The regression equation is Sales = -197 - 0.00063 outlets + 1.74 automobiles + 0.410 income + 2.04 age - 0.034 bosses SE Predictor Coefficient Coefficient I Constant -19.672 5.422 -3.63 8. 022 Outlets -0.908629 0.082638 -0. 24 8. 823 Automobiles 1.7399 0.5530 3.15 8. 035 Income 9. 40994 9. 04385 9.35 0. 981 Age 2.0357 0.8779 2.32 9. 981 Bosses -0.0344 9.1889 -9. 18 9. 864 Analysis of Variance Source DF SS MS Regression 1, 593.81 318.76 140.36 0.9091 Residual Error 9.08 2.27 Total 1602.89 c. Conduct a global test of hypothesis to determine whether any of the regression coefficients are not zero. Use the 0.05 significance level. (Round your answer to 2 decimal places.) Ho is The computed value of F isd. Conduct a test of hypothesis on each of the Independent variables. Would you consider eliminating "outlets" and "bosses"? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) "outlets" and "bosses". Critical values are and e. The regression has been rerun below with "outlets" and "bosses" eliminated. Compute the coefficient of determination. How much R- has changed from the previous analysis? (Round your answer to 4 decimal places.) The regression equation is Sales = -18.9 - 1.61 automobiles - 0.400 Income - 1.96 age SE Predictor Coefficient Coefficient Constant -18.924 3.636 5.20 0.902 Automobiles 1.6129 9.1979 8.15 0.090 Income 9. 49031 9. 81569 25.52 Age 1.9637 0.5846 3.36 0. 015 Analysis of Variance Source OF SS MS Regression 3 1,593.66 531.22 345.25 0. Bee Residual Error 9.23 1.54 Total 1, 602.89 . There was little change in the coefficient of determination. g. Following is a plot of the fitted values of y(1.e., y ) and the residuals. Do you see any violations of the assumptions? 1.2 Residual (y - )) 1.2 8 16 24 32 40 Fitted There is about the plots