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Question
NARRBEGIN: SA_107_109A large auto dealership is interested in determining the number of cars that will be sold in a given quarter. The management of the dealership believes that a relationship can be found between the number of cars sold (Y), the advertised price (
) and the current interest rates (
). Their past experience shows that they tend to have better luck using a non-linear relationship. Below is the output from a regression analysis using the natural logarithm of the variables in the model.| Summary measures | ||||||
| Multiple R | 0.9326 | |||||
| R-Square | 0.8698 | |||||
| Adj R-Square | 0.8498 | |||||
| StErr of Estimate | 0.0259 | |||||
| ANOVA Table | ||||||
| Source | df | SS | MS | F | p-value | |
| Explained | 2 | 0.0581 | 0.0290 | 43.4187 | 0.0000 | |
| Unexplained | 13 | 0.0087 | 0.0007 | |||
| Regression coefficients | ||||||
| Coefficient | Std Err | t-value | p-value | |||
| Constant | 4.3965 | 0.7549 | 5.8239 | 0.0001 | ||
| Log Price | -0.8255 | 0.2467 | 3.3456 | 0.0053 | ||
| Log Interest | -0.1225 | 0.1880 | -0.6512 | 0.5262 | | |
(A) Use the information above to estimate the regression model.
(B) Interpret each of the estimated regression coefficients of the regression model in (A).
(C) Does using a non-linear model seem to be a good choice in this example? Explain your answer.
Answer
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