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Question
NARRBEGIN: SA_88_93A company that makes baseball caps would like to predict the sales of it main product, standard little league caps. The company has gathered data on monthly sales of caps at all of its retail stores, along with information related to the average retail price, which varies by location. Below you will find regression output comparing these two variables.
| Summary measures | |
| Multiple R | 0.5892 |
| R-Square | 0.3472 |
| StErr of Estimate | 10283.97 |
| ANOVA table | |||||
| Source | df | SS | MS | F | p-value |
| Explained | 1 | 899825600 | 899825600 | 8.5082 | 0.0101 |
| Unexplained | 16 | 1692159250 | 105759953 | ||
| Regression coefficients | |||||
| Coefficient | Std Err | t-value | p-value | ||
| Constant | 147984.44 | 28831.21 | 5.1328 | 0.0001 | |
| Average Price | -7370.94 | 2527.00 | -2.9169 | 0.0101 | |
(A) Estimate the regression model. How well does this model fit the given data?
(B) Is there a linear relationship between X and Y at the 5% significance level? Explain how you arrived at your answer.
(C) Use the estimated regression model to predict the number of caps that will be sold during the next month if the average selling price is $10.
(D) Find a 95% prediction interval for the number of caps determined in Question 90. Use t- multiple = 2.
(E) Find a 95% confidence interval for the average number of caps sold given an average selling price of $10. Use a t-multiple = 2.
(F) How do you explain the differences between the widths of the intervals in (D) and (E)?
Answer
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