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
26	139	2,371	26	146	3,290
25	132	2,226	25	144	3,103
27	144	2,731	27	147	2,122
27	142	3,351	25	144	2,791
27	142	2,289	25	149	3,209
28	142	3,449	25	131	2,287
33	138	3,114	27	144	2,848
28	139	3,342	25	132	2,690
29	144	2,842	29	132	2,933
27	134	2,625	28	127	2,671
28	135	2,121	27	154	2,988
27	137	2,219	26	147	2,829
28	146	3,463

  Click here for the Excel Data File

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?

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

Answer 1

Solution:

Using the given data we solve this problem using the statistical software as below

the regresion model is

Commissions ($000) = -101.3 + 0.887 Calls + 0.0502 Driven - 0.000347 Calls*Driven

now Table will below

Compute the value of the test statistic corresponding to the interaction term.

Ans: F value = 4.49

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

now

Hypothesis

H0: interaaction term is not significant .

vs

H1 : interaaction term is significant .

Ans : Here p value is 0.046 which is less than 0.05 therefore we reject null hypothesis

therefore we say that the interaction term is statistical significant so we conclude that there is interaction.

Thank You..!!

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