Question

In: Statistics and Probability

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The...

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.)

Solutions

Expert Solution

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

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