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Unformatted text preview: Econ 103 UCLA, Fall 2010 Problem Set 2 Due: Thursday, October 14 in hardcopy at the beginning of class Note: Please attach the Homework Cover Page from Classweb to the front of your home- work. Part 1: True or False and explain briefly why. 1. To obtain the slope estimator using the least squares principle, we divide the sample covariance of X and Y by the sample variance of Y . 2. The OLS intercept coefficient is equal to the average of the Y i in the sample. 3. Among all unbiased estimators that are weighted averages of Y 1 ,...,Y n , 1 is the most unbiased estimator of 1 . 4. When the estimated slope coefficient in the simple regression model, 1 is zero, then R 2 = 0 . 5. The standard error of the regression is equal to 1- R 2 . 6. Heteroskedasticity is when the variance of u i depends on the value of X i . 7. The output from the Stata command regress y x reports the p-value associated with the test of the null hypothesis that 1 = 0 . 8. ESS=SSR+TSS. 9. In the simple regression we can compute R 2 as Cov ( X,Y ) Y X 2 10. The sample average of the OLS residuals is zero. 11. Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the OLS estimate of the slope the same. 12. Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the regression R 2 the same. 13. In the presence of heteroskedasticity, and assuming that the usual least squares as- sumptions hold, the OLS estimator is unbiased and consistent, but not BLUE. 14. The t-statistic is calculated by dividing the estimator minus its hypothesized value by the standard error of the estimator. 1 Econ 103 UCLA, Fall 2010 15. The 95% confidence interval for 1 is the interval h 1- 1 . 96 SE ( 1 ) , 1 + 1 . 96 SE ( 1 ) i . Part 2: Analytical questions. Question 1: You have obtained a sub-sample of 1744 individuals from the Current Popula- tion Survey (CPS) and are interested in the relationship between weekly earnings and age. The regression, using heteroskedasticity-robust standard errors, yielded the following result: Earnings = 239 . 16 (20 . 24) + 5 . 20 (0 . 57) Age , R 2 = 0 . 05 , SER = 287 . 21 where Earnings and Age are measured in dollars and years respectively....
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This note was uploaded on 10/23/2010 for the course STATISTICS 2 taught by Professor Ramirez during the Winter '09 term at USC.
- Winter '09