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:

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.)

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.)

At the .05 significance level is there a significant interaction between the number of sales calls and the miles driven?

• 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)

Explanation / Answer

following information has been generated using the given data

(first part) Commissions = 25.1558-0.0938 Calls-0.0151 Miles + 0.000157X1X2

(second part)

(third part) test statistic of interaction is given as

t=X1X2coefficient/SE(X1X2)=0.000157/0.0002407=0.65

since p-value of intearaction =0.5213 is more than level of signifiance alpha=0.05, so it is not significant.

Analysis of Variance Source DF Sum of Mean F Value p-value Squares Square Model 3 1933.4595 644.48651 4.54 0.0133 Error 21 2980.5405 141.9305 Corrected Total 24 4914 Root MSE 11.9135 R-Square 0.3935 Dependent Mean 33 Adj R-Sq 0.3068 Coeff Var 36.1014 Parameter Estimates Variable DF Parameter Standard t Value p-value Estimate Error Intercept 1 25.15581 93.08781 0.27 0.7896 X1 1 -0.0938 0.65887 -0.14 0.8882 X2 1 -0.0151 0.0336 -0.45 0.6578 X1X2 1 0.000157 0.0002407 0.65 0.5213

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