The sales manager of a large automotive parts distributor wants to estimate the total annual sales for each of the compa

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The Sales Manager Of A Large Automotive Parts Distributor Wants To Estimate The Total Annual Sales For Each Of The Compa 1 (112.98 KiB) Viewed 36 times

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 retall 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 retall 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. Annual Sales (S Number of millions), y 37.702 24.196 32.055 3.611 17.625 45.919 29.600 8.114 20.116 12.994 outlets automobiles income age bosses Retail outlets, Predictor Constant outlets Automobiles Income Age Bosses X1 1,739 1,221 1,846 120 1,096 2,290 1,687 241 649 1,427 Regression Residual Error Total Number of Automobiles Registered (millions), x₂ 9.27 5.86 8.81 3.81 10.31 -19.672 -0.000629 1.7399 0.40994 2.0357 -0.0344 Analysis of variance Source 11.62 8.96 6.28 7.77 10.92 sales outlets cars income age 8.899 0.605 8.775 0.964 0.825 0.409 -0.323 0.256 SE Coefficient coefficient t 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? DF Personal Income Average Age of (5 billions), Automobiles (years), X4 X3 85.4 60.7 68.1 20.2 33.8 95.1 -0.489 -0.447 -0.349 0.183 0.395 0.155 0.291 5 4 9 69.3 16.3 34.9 15.1 SS 1,593.81 9.08 1602.89 P 0.022 5.422 -3.63 0.002638 -0.24 0.823 0.5530 3.15 0.035 0.04385 9.35 0.001 0.8779 e.isse 2.32 0.081 -0.18 0.864 The strongest relationship is between sales and income Also, outlets and income are strongly correlated. This is called b. 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-19.7 -0.00063 outlets +1.74 automobiles + 0.410 Income +2.04 age-0.034 bosses ♡ 3.5 5.0 4.4 4.0 3.5 4.1 4.1 5.9 5.5 4.1 Number of Supervisors, x5 A problem multicollinearity MS F P 318.76 140.36 0.0001 2.27 9.0 5.0 7.0 5.0 7.0 13.0 15.0 Answer is complete and correct. could occur 11.0 16.0 10.0 if both "cars" and "outlets" are part of the final solution 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 rejected Delete d. 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.) Predictor Constant Automobiles Income Age Regression. Residual Error Total Answer is not complete. The computed value of F "outlets" and "bosses". Critical values are e. The regression has been rerun below with "outlets" and "bosses" eliminated. Compute the coefficient of determination. How much R² 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 0.40031 1.9637 Analysis of variance Source SE Coefficient coefficient t -18.924 1.6129 OF 3 6 9 Answer is not complete. P 3.636 -5.20 0.002 e.1979 8.15 0.000 0.01569 25.52 0.000 0.5846 3.36 0.015 SS MS P 1,593.66 531.22 345.25 0.000 1.54 9.23 1,602.89 and There was little change in the coefficient of determination.