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)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
The previous answer I received was incorrect. I still need help with this. Thank You!
Here are the previous answers:
From the output, the intercept is -322.071, coefficient for calls is 2.203, coefficient for miles is 0.0970, and coefficient for interaction is -0.001.
Thus, the regression equation including an interaction term isCommissions=−322.071+2.203 Calls+0.097 Miles−0.001 x1x2Commissions=-322.071+2.203 Calls+0.097 Miles-0.001 x1x2.
The value of the test statistic corresponding to the interaction term is -1.365.
Decision rule:
If p-value≤α≤α, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.
Conclusion:
The p-value (0.187) is greater than the level of significance (0.05).
Based on decision rule, fail to reject the null hypothesis.
Thus, the not significant interaction between the number of sales call and the miles driven.
![**Regression Analysis Exercise**
**Equation for Commissions:**
\[ \text{Commissions} = \_\_ + \_\_ \times \text{Calls} + \_\_ \times \text{Miles} + \_\_ \times \text{x1x2} \]
**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.)*
\[ \text{Value of the test statistic} = \_\_ \]
**Question:**
At the 0.05 significance level, is there a significant interaction between the number of sales calls and the miles driven?
\[ \text{This is } \_\_ , \text{ so we conclude that there is } \_\_. \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb299a4ab-95e2-40fd-810f-07b7412657e7%2F712528ee-f0cb-4773-be75-09be5939df2e%2Fd8wgd6s_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
