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
32	150	2,672	38	147	3,290
13	132	2,226	44	144	3,103
33	145	2,732	49	148	2,123
38	143	3,351	38	144	2,791
23	143	2,290	37	150	3,210
47	143	3,449	14	131	2,287
29	138	3,114	34	145	2,848
38	139	3,343	25	133	2,691
41	145	2,843	27	132	2,933
32	135	2,625	25	127	2,672
25	143	2,300	43	155	2,988
13	137	2,220	34	147	2,829
47	146	3,463

1.

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

2.

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

3.

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:_______

Answer 1

Applying regression:

1)Commission =-648.764+4.570*Calls+0.210*Miles+(-0.001)*x1x2
2)

	Coefficients	Standard Error	t Stat	P-value
Intercept	-648.764	209.305	-3.100	0.005
Calls	4.570	1.476	3.096	0.005
Driven	0.210	0.077	2.732	0.012
x1x2	-0.001	0.001	-2.580	0.017

3)

Value of the Test Statistic =-2.58