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Unformatted text preview: Solutions, Chapter 2/HL 1 ANSWERS TO CHAPTER 2 The Simple Regression Model Econometrics Economics of Innovation and Growth A = Problems B = Examples (from chapter 2) C = Cumputer Exercises Solutions, Chapter 2/HL 2 A: Problems 2.1 Let kids denote the number of children born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is u educ kids + + = 1 where u is the unobserved error. (i) What kind of factors are contained in u? Are these likely to be correlated with level of education? (ii) Will a simple regression analysis uncover ceteris paribus effects of education on fertility? Explain. (i) Income, age, and family background (such as number of siblings) are just a few possibilities. It seems that each of these could be correlated with years of education. (Income and education are probably positively correlated; age and education may be negatively correlated because women in more recent cohorts have, on average, more education; and number of siblings and education are probably negatively correlated.) (ii) Not if the factors we listed in part (i) are correlated with educ . Because we would like to hold these factors fixed, they are part of the error term. But if u is correlated with educ then E( ueduc ) 0, and so SLR.3 fails.  2.2 In the simple linear regression model y= + 1 x + u, suppose that E(u) 0. Letting 0=e(u), show that the model can always be rewritten with the same slope, but new intercept and error, where the new error has a zero expected value. Answers In the equation y = + 1 x + u , add and subtract from the right hand side to get y = ( + ) + 1 x + ( u ). Call the new error e = u , so that E( e ) = 0. The new intercept is + , but the slope is still 1 . Solutions, Chapter 2/HL 3 2.3 The following table contains the ATC scores and the GPA (grade point average) for 8 college students. Grade point average is based on a fourpoint scale and has been rounded to the one digit after the decimal. Student GPA ACT 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 39 6 3.0 25 7 2.7 25 8 3.7 30 (i) Estimate the relationship between GPA and ACT using ols; that is, obtain the intercept and slope in the equation ACT A P G 1 + = Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is GPA predicted to be if the ACT score is increased by 5 points? (ii) Compute the fitted valued and the residuals for each observation, and verify that the residuals (approximately) sum to zero....
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This note was uploaded on 08/09/2009 for the course ECON 120B taught by Professor Jeon during the Spring '08 term at UCSD.
 Spring '08
 Jeon
 Econometrics

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