Thank you Cincinnati Paint Company sells quality brands of paints through hardwa

Question

Thank you

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 seeded a sample of 25 sales representatives and determined: The amount earned in commissions last month (Y) The number of miles driven last month (X_2) The number of sales calls made last month (X_1) The information is reported below. Develop a regression equation including an interaction term. Complete the following table. Compute the value of the test statistic corresponding to the interaction term. At the.05 significance level is there a significant interaction between the number of sales calls and the miles driven?

Explanation / Answer

First of all you need to create an additional column for the interaction terms i.e. X1X2.

Just multiply the values of the two variables to get the data as shown below -

Now, Run the Linear regression in your excel file by using following steps -

Go to the "Data" tab from the top ---> Then on the right top corner you will get a button for "Data Analysis". Click on it and you will be given a list of things----> Select Regression from the drop down menu---> Then in the input range enter the range of the data to get the output.

Following is the output obtained from excel for the given dataset -

So, We can write the equation as -

Y = 97.00826 - 0.56687(X1) - 0.03176(X2) + 0.00025(X1X2)

Or, we can write it as -

Commisions = 97.00826 - 0.56687 (Calls) - 0.03176 (Miles) + 0.00025 (X1X2)

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The second table can be filled with the output obtained from excel as shown -

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As we can see from the above table that the test statistic corresponding to the interaction term is - T = 1.47, so value of test statistic = 1.47

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The hypothesis for the significance test of interaction is -

Null Hypothesis - The Variable (interaction) is insignificant (i.e. Its coefficient is not significantly different from 0)

Alternate Hypothesis - The Variable (interaction) is significant (i.e. Its coefficient is significantly different from 0).

The P-value corresponding to the test statistic of the interaction term (X1X2) is = p = 0.156.

So, we would fail to reject the null hypothesis and conclude that there is no significance interaction between number of sales calls and miles driven.

Commissions ($000) - Y Calls - X1 Driven - X2 Interaction - X1*X2 24 127 2279 289433 26 128 2137 273536 22 129 2683 346107 21 129 3284 423636 22 129 2221 286509 20 131 3382 443042 20 135 3040 410400 32 114 3270 372780 28 117 2762 323154 19 146 2589 377994 22 184 2088 384192 27 136 2142 291312 29 104 3393 352872 22 114 3229 368106 14 116 3061 355076 32 117 2044 239148 25 143 2735 391105 24 143 3137 448591 16 159 2250 357750 29 160 2793 446880 45 166 2623 435418 34 167 2875 480125 29 168 2588 434784 40 185 2934 542790 44 141 2762 389442

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