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	141	2,372	39	146	3,293
14	132	2,229	44	146	3,106
33	144	2,732	30	148	2,122
38	144	3,352	38	144	2,793
24	144	2,289	37	150	3,209
48	142	3,452	14	131	2,289
30	139	3,116	35	145	2,850
39	141	3,342	25	132	2,693
42	144	2,845	28	133	2,933
32	136	2,625	26	129	2,673
21	137	2,124	43	154	2,989
14	138	2,222	34	148	2,831
47	148	3,463

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

Comissions= ______+_______ calls +__________ Miles +__________

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.)

Answer 1

In order to solve this question I used Excel.

Step.1 Enter data in excel sheet.

Step.2 Go to 'Data' menu ---> 'Data Analysis' ---> Select 'Regression'.

Step.3 New window will pop-up on screen. Refer following screen shot and enter information accordingly.

Interaction = calls * Driven

Excel output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9227774
R Square	0.85151814
Adjusted R Square	0.83030644
Standard Error	4.13706326
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	3	2061.21886	687.072953	40.1438046	7.0633E-09
Residual	21	359.42114	17.1152924
Total	24	2420.64
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-340.66138	154.940237	-2.1986631	0.03924788	-662.87724	-18.445514
Calls	2.32210571	1.09370365	2.12315805	0.04579213	0.04762445	4.59658696
Driven	0.10441515	0.05698154	1.83243837	0.08110578	-0.0140844	0.22291474
Interaction	-0.000625	0.00040034	-1.5612601	0.133407	-0.0014576	0.00020752

Regression equation :

Commission = -340.661 + 2.322 Calls + 0.104 Driven _ 0.001 X1X2

Predictor	Coefficients	SE coefficients	t	p-value
Constant	-340.661	154.940	-2.20	0.039
Calls	2.322	1.094	2.12	0.046
Driven	0.104	0.057	1.83	0.081
Interaction	-0.001	0.000	-1.56	0.133