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)CallsDrivenCommissions ($000)CallsDriven23682,372391883,29114302,229442183,103341362,733291052,123391803,353381622,79424772,291371543,209471863,45115252,289301033,117341322,850391433,34326942,692422002,84328962,934321562,62625812,67321502,122442052,98813462,222351552,830472253,466 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.) PredictorCoefficientSE Coefficienttp-valueConstant 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.) At the 0.05 significance level, is there a significant interaction between the number of sales calls and the miles driven?

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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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
23	68	2,372	39	188	3,291
14	30	2,229	44	218	3,103
34	136	2,733	29	105	2,123
39	180	3,353	38	162	2,794
24	77	2,291	37	154	3,209
47	186	3,451	15	25	2,289
30	103	3,117	34	132	2,850
39	143	3,343	26	94	2,692
42	200	2,843	28	96	2,934
32	156	2,626	25	81	2,673
21	50	2,122	44	205	2,988
13	46	2,222	35	155	2,830
47	225	3,466

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.)

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

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