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 (X2) • The number of sales calls made last month (X1) The information is reported below. Commissions ($000) Calls Driven Commissions ($000) Calls Driven 14 129 2,288 28 109 3,217 18 131 2,162 24 129 3,035 24 131 2,647 28 132 2,070 20 143 3,275 32 164 2,726 24 143 2,205 36 176 3,119 14 159 3,395 38 181 2,235 16 160 3,039 39 183 2,771 22 116 3,283 41 189 2,595 14 121 2,772 42 196 2,897 18 157 2,564 35 137 2,593 20 192 2,058 33 157 2,927 22 107 2,139 44 104 2,770 20 109 3,379 PictureClick here for the Excel Data File Develop a regression equation including an interaction term. (Round your answers to 5 decimal places. Negative amounts should be indicated by a minus sign.) Commissions = + Calls + Miles + X1X2 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.) Predictor Coef SE Coef T P Constant Calls Miles X1X2 Compute the value of the test statistic corresponding to the interaction term. (Round your answer to 2 decimal places. Negative amount should be indicated by a minus sign.) Value of the test statistic At the .05 significance level is there a significant interaction between the number of sales calls and the miles driven? This is , so we conclude there .

Explanation / Answer

the regression equation is given as

y=15.04254+0.07243x1-0.00240x2+0.00002x1x2

the p-value of interaction x1x2 =0.908 is more than alpha=0.05, so it is not significant

following information has been generated using ms-excel

Analysis of Variance Source DF Sum of Mean F Value p-va;ie Squares Square Model 3 302.57833 100.8594 1.12 0.3635 Error 21 1891.18167 90.05627 Corrected Total 24 2193.76 Root MSE 9.4898 R-Square 0.1379 Dependent Mean 26.64 Adj R-Sq 0.0148 Coeff Var 35.6224 Parameter Estimates Variable DF Parameter Standard t Value p-value Estimate Error Intercept 1 15.04254 64.53096 0.23 0.818 x1 1 0.07243 0.44548 0.16 0.872 x2 1 -0.0024 0.02341 -0.1 0.919 x1x2 1 0.00001904 0.000163 0.12 0.908

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