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Unformatted text preview: Econ 103 UCLA, Spring 2011 Problem Set 2 Due: Tuesday, April 19 in hardcopy at the beginning of class Note: Please attach the Homework Cover Page , which you can download from the class website, to the front of your homework. Part 1: True or False and explain brie y 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 coe cient ˆ β 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 , ˆ β 1 is the most unbiased estimator of β 1 . 4. When the estimated slope coe cient in the simple regression model, ˆ β 1 is zero, then R 2 = 0 . 5. The standard error of the regression is equal to 1- R 2 . 6. The output from the Stata command regress y x reports the p-value associated with the test of the null hypothesis that β 1 = 0 . 7. ESS=SSR+TSS. 8. The sample average of the OLS residuals is zero. 9. 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. 10. The t-statistic is calculated by dividing the estimator minus its hypothesized value by the standard error of the estimator. 11. The 95% con dence interval for β 1 is the interval h ˆ β 1- 1 . 96 SE ( ˆ β 1 ) , ˆ β 1 + 1 . 96 SE ( ˆ β 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 yielded the following result (standard errors in parenthesis): 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. 1 Econ 103 UCLA, Spring 2011 (a) Interpret the results. (b) Is the e ect of age on earnings large? (c) Why should age matter in the determination of earnings? Do the results suggest that there is a guarantee for earnings to rise for everyone as they become older? Do you think that the relationship between age and earnings is linear?...
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