Question
In: Economics
The data file "supermarket.csv" contains data on the total amount of eggs sold, relevant prices and...
The data file "supermarket.csv" contains data on the total amount of eggs sold, relevant prices and advertising information at a supermarket.
1) Treating the data as linear, run a multivariate regression of total egg sales on the three other variables.
2) Perform a log-log transformation of the data (Achieved by taking the natural logarithm of all variables except ad type). Run a multivariate regression of log total egg sales on log egg prices and log cookie prices (discard the dummy variable for ad type).
3) Compare the Lerner index values from parts 1 and 2. In your opinion, which method is more accurate? Why?
4) Interpret the Lerner index you chose in part 3. What percentage of the supermarkets price is their prot margin.
My data is below. There is 4 column in the data which are Sales, Price.eggs, Ad.Type, and Price.Cookies.
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Solutions
Expert Solution
| 1) | |||||||||
| SUMMARY OUTPUT | |||||||||
| Regression Statistics | |||||||||
| Multiple R | 0.941103 | ||||||||
| R Square | 0.885675 | ||||||||
| Adjusted R Square | 0.872483 | ||||||||
| Standard Error | 2.610661 | ||||||||
| Observations | 30 | ||||||||
| ANOVA | |||||||||
| df | SS | MS | F | Significance F | |||||
| Regression | 3 | 1372.796 | 457.5986 | 67.14038 | 2.25E-12 | ||||
| Residual | 26 | 177.2043 | 6.815549 | ||||||
| Total | 29 | 1550 | |||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | ||
| Intercept | 137.3699 | 10.83371 | 12.67985 | 1.22E-12 | 115.1009 | 159.6389 | 115.1009 | 159.6389 | |
| Peggs | -16.1184 | 1.645593 | -9.79491 | 3.26E-10 | -19.501 | -12.7359 | -19.501 | -12.7359 | |
| Adtype | 4.147389 | 1.039658 | 3.989187 | 0.000481 | 2.010342 | 6.284436 | 2.010342 | 6.284436 | |
| Pcookies | -8.71078 | 1.901333 | -4.58141 | 0.000101 | -12.619 | -4.80254 | -12.619 | -4.80254 | |
| 2) | ||||||||||
| SUMMARY OUTPUT | ||||||||||
| Regression Statistics | ||||||||||
| Multiple R | 0.933279 | |||||||||
| R Square | 0.87101 | |||||||||
| Adjusted R Square | 0.856127 | |||||||||
| Standard Error | 0.089706 | |||||||||
| Observations | 30 | |||||||||
| ANOVA | ||||||||||
| df | SS | MS | F | Significance F | ||||||
| Regression | 3 | 1.412809 | 0.470936 | 58.52204 | 1.07E-11 | |||||
| Residual | 26 | 0.209226 | 0.008047 | |||||||
| Total | 29 | 1.622035 | ||||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||
| Intercept | 8.322894 | 0.537063 | 15.49704 | 1.2E-14 | 7.218945 | 9.426844 | 7.218945 | 9.426844 | ||
| ln_Peggs | -2.07033 | 0.239576 | -8.64166 | 4.04E-09 | -2.56279 | -1.57788 | -2.56279 | -1.57788 | ||
| Ad_type | 0.152622 | 0.035588 | 4.288587 | 0.00022 | 0.07947 | 0.225774 | 0.07947 | 0.225774 | ||
| ln_Pcookies | -1.32383 | 0.287994 | -4.59674 | 9.75E-05 | -1.91581 | -0.73185 | -1.91581 | -0.73185 | ||
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