midterm%20exam%20solutions%202011 - Econ 120B Patrik...

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Econ 120B, Patrik Guggenberger, Department of Economics, UCSD April 29th, 2010 Midterm, Type A Please answer all questions. You have 80 minutes to work on the exam. best: 1) Assume in the simple linear regression model Y i = & 0 + 1 X i + u i , Y i is constant for all the datapoints ( Y i ;X i ) i = 1 ;:::;n: Then i) 0 < R 2 < 1 ii) R 2 = Y iii) R 2 > ( SSR=TSS ) iv) R 2 = 0 See question 18 on homework 2. As the previous version of the homework the question is wrongly formulated. 2) Under perfect multicollinearity i) the OLS estimator is biased even in samples of sample size > 100. ii) the OLS estimator cannot be computed. iii) the error terms are highly, but not perfectly, correlated. iv) an intercept should always be included in the regression. As discussed in class, the OLS estimator cannot be computed in this case as The OLS estimator is not unique. 3) One key di/erence between the multiple linear regression model and the nonlinear polynomial regression model is that i) the coe¢ cient of a regressor in the linear model has an interpretation as the expected change in the regressand when the regressor changes by one unit - holding all the other regressors constant; but this interpretation does not generally hold in the nonlinear model ii) the expected change in the regressand is typically larger in the nonlinear model when changing a regressor by one unit iii) the model is nonlinear in the coe¢ cients in the nonlinear model but linear in the coe¢ cients in the linear model iv) the linear model can be estimated using OLS but this is not true for the nonlinear model. Not relevant yet. Part II: 1) Data were collected from a random sample of 220 home sales from a community in 2003. Let Price denote the selling price (in $1000), BDR denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet), Lsize denote the lot size (in square feet), 1
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This note was uploaded on 11/28/2011 for the course HIST 15 taught by Professor Patch during the Spring '08 term at UC Riverside.

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midterm%20exam%20solutions%202011 - Econ 120B Patrik...

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