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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 pvalue 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 tstatistic 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 subsample 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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 Spring '07
 SandraBlack
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