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:
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 | 140 | 2,372 | 38 | 146 | 3,291 |
| 13 | 132 | 2,227 | 44 | 145 | 3,104 |
| 33 | 145 | 2,732 | 29 | 147 | 2,122 |
| 38 | 146 | 3,351 | 38 | 144 | 2,792 |
| 23 | 142 | 2,289 | 37 | 149 | 3,210 |
| 47 | 143 | 3,450 | 14 | 132 | 2,288 |
| 29 | 138 | 3,114 | 34 | 144 | 2,848 |
| 38 | 146 | 3,342 | 25 | 132 | 2,691 |
| 41 | 145 | 2,843 | 27 | 132 | 2,934 |
| 32 | 134 | 2,626 | 25 | 128 | 2,672 |
| 20 | 136 | 2,121 | 43 | 154 | 2,989 |
| 13 | 137 | 2,220 | 34 | 147 | 2,829 |
| 47 | 146 | 3,464 | |||
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.)
Complete the following table. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
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?
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