Question

Cincinnati Paint Company sells quality brands of paints through hardware stores throughout the United States. The company maintains a large sales force whose job it is to call on existing customers as well as 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:

Commissions	Calls	Driven
22	143	2374
13	136	2227
34	146	2733
39	142	3351
23	142	2293
47	146	3450
30	141	3117
38	139	3344
42	148	2843
33	138	2629
20	138	2124
14	138	2223
47	150	3465
39	149	3291
45	145	3106
30	149	2125
39	145	2792
37	153	3213
15	135	2287
34	146	2851
25	133	2690
28	132	2936
26	130	2671
43	155	2992
35	148	2830

A) Develop a regression equation including a interaction term.

Answer 1

In regards to this question, first of all I shall find a regression equation between the Calls made and the Distance driven in order to find a relationship between these two variables.

After this, a multiple regression equation will be derived in order to find the relationship between the three variables.

Part A:

Relationship between the Number of Sales calls made and the Miles Driven by the Sales Representative

Please find the output as derived from Excel...

The regression equation will be:

Miles Driven = 25.2962 * Calls - 810.98

The relationship between the two variables is not strong as the R squared value is not closer to 1. Generally, it should be closer to 1 in order to represent a strong relationship.

In this case, the value of R squared is 0.1499 that that means only 14.99% of the variations of the data is explained by the regression model which doesn't represent a healthy relationship.

Part B:

In order to investigate whether sales representatives who drive the most miles and make the most calls necessarily earn the most in sales commissions, we need to perform a multiple regression.

The output of the multiple regression as derived in Excel is shown below:

Here, Commission is taken as the independent variable and the Calls as well as the Miles Driven is considered as the independent variable.

Here, the regression equation is Commission = 0.616 * Calls + 0.015891 * Driven Miles - 100.449

Here, the R squared value is closer to 1 or more than 0.75 and hence it can be stated that there is a strong relationship between the Calls made and the distance travelled with that of the total commissions received.

In this case, the value of the R squared is 0.8266 is more than 75% or 0.75. this means that 82.66% of the variations of the data is explained by the regression model which represents a strong relationship between the dependent and the independent variables.

It can also be concluded that the Total Calls made and the Miles Travelled by the sales representative has a strong relation ship with the Commission received or in other words it can also be stated that the Total Calls made and the Miles Travelled by the sales representative has a strong impact on the Commission received by them.

End of the Solution...