Cincinnati Paint Company sells quality brands of paints through hardware stores
ID: 3228026 • Letter: C
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 (X1) • The number of sales calls made last month (X2) The information is reported below.
1
Develop a regression equation including an interaction term. (Round your answers to 3 decimal places.Negative amounts should be indicated by a minus sign.)
2. Complete the following table. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
3. 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.)
4.
At the .05 significance level is there a significant interaction between the number of sales calls and the miles driven?
Commissions Calls Driven 22 139 2371 13 132 2226 33 144 2731 38 142 3351 23 142 2289 47 142 3449 29 138 3114 38 139 3342 41 144 2842 32 134 2625 20 135 2121 13 137 2219 47 146 3463 38 146 3290 44 144 3103 29 147 2122 38 144 2791 37 149 3209 14 131 2287 34 144 2848 25 132 2690 27 132 2933 25 127 2671 43 154 2988 34 147 2829Explanation / Answer
The statistical software output for this problem is:
Multiple linear regression results:
Dependent Variable: Commissions
Independent Variable(s): Calls, Driven, Calls * Driven
Commissions = -314.63626 + 2.1502997 Calls + 0.094104073 Driven + -0.0005564387 Calls * Driven
Parameter estimates:
Analysis of variance table for multiple regression model:
Summary of fit:
Root MSE: 4.2347001
R-squared: 0.8479
R-squared (adjusted): 0.8262
Hence,
1. Commissions = -314.636 + 2.150 Calls + 0.094 Driven + -0.001 X1X2
2. Table:
3. Value of test statistic = -1.32
4. This is not significant so we conclude there is no interaction.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -314.63626 162.64986 0 21 -1.9344392 0.0666 Calls 2.1502997 1.1587172 0 21 1.855759 0.0776 Driven 0.094104073 0.059442478 0 21 1.5831116 0.1283 Calls * Driven -0.0005564387 0.00042152402 0 21 -1.320064 0.201