Question

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force who call on existing customers and 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.

Commissions ($000)	Calls	Driven	Commissions ($000)	Calls	Driven
22	64	2,371	38	167	3,290
13	51	2,226	44	168	3,103
33	129	2,731	29	108	2,124
38	141	3,353	38	164	2,792
23	78	2,292	37	177	3,210
48	224	3,451	14	25	2,287
29	95	3,115	34	160	2,850
39	169	3,344	25	81	2,692
42	188	2,843	28	83	2,934
33	126	2,627	25	85	2,671
21	53	2,122	44	194	2,990
14	56	2,221	35	137	2,832
48	176	3,464

Develop a regression equation including an interaction term. (Negative amount should be indicated by a minus sign. Round your answers to 3 decimal places.)

Commissions= ______ + ______ calls + _______ miles + ______ x1x2

Complete the following table. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Predictor	Coefficient	SE Coefficient	t	p-value
Constant
Calls
Miles
X1X2

Compute the value of the test statistic corresponding to the interaction term. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Value of the test statistic ________

At the 0.05 significance level is there a significant interaction between the number of sales calls and the miles driven?

This is _____________(statistically significant/not statistically significant) , so we conclude that there ____________ (is interaction/ is no interaction)

Answer 1

Applying regression from excel: data -data analysis: regression:

Commissions=-10.244+0.239*Calls+0.009*miles+(-0.000)*x1x2

	Coefficients	Standard Error	t Stat	P-value
Intercept	-10.244	10.266	-0.998	0.330
Calls	0.239	0.083	2.878	0.009
Driven	0.009	0.004	2.073	0.051
x1x2	0.000	0.000	-1.071	0.296

  value of the test statistic = -1.07

This is not statistically significant o we conclude that there  is no interaction