Problem Set 2

Problem Set 2 - Economics 103 Winter 2009 Problem Set 2 Due...

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Economics 103 Winter 2009 Problem Set 2 Due Tuesday, February 3 Question 1: True/False/Explain 1. When the estimated slope coefficient in the simple regression model, 1 ö β , is zero, then R 2 =0. 2. The variance of Y i is equal to the variance of the error term in the regression. 3. To obtain the slope estimator using the least squares principle, you divide the sample covariance of X and Y by the sample variance of Y 4. The population regression line and the sample regression line are the same on average. 5. We do not need any assumptions in order for OLS estimators to be BLUE (Best linear unbiased estimator) 6. The model y= α + β log(x) is linear in the variables but not linear in the parameters. It therefore satisfies our linearity assumption. 7. If the p-value for a two-sided test is .03, you fail to reject the null hypothesis at the 5% confidence level. 8. The assumptions made by the classical linear regression model (CLRM) are not necessary to compute OLS estimators. Question 2 Show that OLS estimators are unbiased. (Use a simple bivariate regression function.) What assumptions do you need? Question 3 Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19 th century. It is from this study that the name “regression” originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship (Standard errors in parenthesis):
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± Studenth = 19.6 + 0.73× Midparh , R 2 = 0.45 (7.2) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. (Following Galton’s methodology, both variables were adjusted so that the average female height was equal to the average male height.) 1. Interpret the estimated coefficients. 2.
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Problem Set 2 - Economics 103 Winter 2009 Problem Set 2 Due...

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