Cincinnati Paint Company sells quality brands of paints through hardware stores

Question

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as look for new business The national sales manager is investigating the relationship between the number of sales calls made and the miles driven by the sales representative. Also, do the sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions? To investigate, the vice president of sales selected a sample of 25 sales representatives and determined: The amount earned in commissions last month (Y) The number of miles driven last month (X_2) The number of sales calls made last month (X_1) The information is reported below. Develop a regression equation including an interaction term (Round your answers to 5 decimal places. Negative amounts should be indicated by a minus sign.) Complete the following table (Round your answers for Coef, SE Coef to 5 decimal places, T to 2 decimal places and P to 3 decimal places. Negative amounts should be indicated by a minus sign.) At the 05 significance level is there a significant interaction between the number of sales calls and the miles driven?

Explanation / Answer

From the above output from Ms Excel Regression Analysis,

The test statistic for interaction is 1.3096.

This is not significant so we conclude that the interaction should be removed from analysis.

Y X1 X2 X1X2 34000 126 2293 288918 SUMMARY OUTPUT 46000 128 2152 275456 35000 129 2659 343011 Regression Statistics 11000 135 3278 442530 Multiple R 0.302057165 14000 136 2214 301104 R Square 0.091238531 10000 142 3392 481664 Adjusted R Square -0.038584536 32000 143 3046 435578 Standard Error 12319.85162 26000 104 3279 341016 Observations 25 22000 105 2808 294840 10000 144 2547 366768 ANOVA 13000 187 2060 385220 df SS MS F Significance F 12000 115 2160 248400 Regression 3 320006374.8 1.07E+08 0.702791 0.560936 20000 126 3379 425754 Residual 21 3187353625 1.52E+08 31000 132 3195 421740 Total 24 3507360000 26000 133 3036 403788 48000 133 2074 275842 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 44000 149 2714 404386 Intercept 169412.5073 104218.9833 1.625544 0.118961 -47322.7 386147.7 -47322.7 386147.7 42000 153 3154 482562 X1 -969.3661779 740.6732029 -1.30876 0.204757 -2509.68 570.9481 -2509.68 570.9481 16000 167 2214 369738 X2 -53.68813412 38.61373066 -1.39039 0.178972 -133.99 26.61351 -133.99 26.61351 19000 182 2790 507780 X1X2 0.36290529 0.277105353 1.309629 0.204469 -0.21337 0.939177 -0.21337 0.939177 38000 183 2607 477081 26000 188 2879 541252 24000 192 2604 499968 12000 115 2926 336490 18000 132 2768 365376

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