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Unformatted text preview: Midterm 2 Review Part 1: Measure Goodness of Fit The adjusted R2 has been used to select between regression models because of the penalty applied to additional regressors, but the penalty is small. The AIC (Akaike Information Criterion) and the SIC (Schwarz Information Criterion) apply even stronger penalties as more regressors are added. It is important not to fixate too much on adj-R2 AIC, SIC and lose sight of theory and common sense. If economic theory clearly predicts a variable belongs, generally leave it in. You can compare the fit of 2 models (with the same y) by comparing the adj-R2. You cannot use the adj-R2 to compare models with different ys (e.g. y vs. ln(y)). Poor explanatory power has nothing to do with unbiased estimation of the parameters. Poor explanatory power is due to lack of other factors in the model, which is captured in the error. As long as the error, other factors, is not correlated with the independent variables, the estimated parameters are unbiased. Exercise: 1. This question is from the PowerPoint on the blackboard: 660 families are randomly selected and presented the price of ecologically friendly apples and price of regular apples. They are asked how much they would demand given different prices. 1. id respondent identifier 2. educ years schooling 3. date date: month/day/year 4. state home state 5. regprc price of regular apples 6. ecoprc price of ecolabeled apples 7. inseason =1 if interviewed in Nov. 8. hhsize household size 9. male =1 if male 10. faminc family income, thousands 11. age in years 12. reglbs quantity regular apples, pounds 13. ecolbs quantity ecolabeled apples, lbs 14. numlt5 # in household younger than 5 15. num5_17 # in household 5 to 17 16. num18_64 # in household 18 to 64 17. numgt64 # in household older than 64 Answer the following questions: a. Run the regression ecolbs on ecoprc, regprc and report the results in the usual form, including R2 and adjusted R2. Interpret the coefficients on price variables and comment on their signs and magnitudes. b. Are the price variables statistically significant? Report the p-values. c. Do you think the price variables together do a good job of explaining variations in ecolbs? Explain. d. Add the variables faminc, hhsize, educ and age to the regression. Compare the R2 and adjusted R2. What do you conclude? e. Compare the changes on the signs and magnitudes of price variables. Do you think they are unbiased estimators? 2. This question is from the PowerPoint on the blackboard: The file housing contain 546 observations on sales prices of houses sold during July, August and September in the city of Windsor, Canada. Estimate: log(price) = b0 + b1 log(lotsize) + b2 bedrooms + b3 bathrms + b4 airco By adding the remaining variables in the model, discuss how the performance of the model has improved based on R2, adj-R2, AIC and SIC....
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- Spring '08