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empir_ex04[1] - Chapter 4 Linear Regression with One...

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Chapter 4 Linear Regression with One Regressor Solutions to Empirical Exercises 1. (a) AHE = 3.32 + 0.45 × Age Earnings increase, on average, by 0.45 dollars per hour when workers age by 1 year. (b) Bob’s predicted earnings = 3.32 + 0.45 × 26 = $11.70 Alexis’s predicted earnings = 3.32 + 0.45 × 30 = $13.70 (c) The R 2 is 0.02.This mean that age explains a small fraction of the variability in earnings across individuals. 2. (a) Course Evaluation Beauty Index -2 -1 0 1 2 2 3 4 5 There appears to be a weak positive relationship between course evaluation and the beauty index. (b) _ Course Eval = 4.00 + 0.133 × Beauty . The variable Beauty has a mean that is equal to 0; the estimated intercept is the mean of the dependent variable ( Course_Eval ) minus the estimated slope (0.133) times the mean of the regressor ( Beauty ). Thus, the estimated intercept is equal to the mean of Course_Eval . (c) The standard deviation of Beauty is 0.789. Thus Professor Watson’s predicted course evaluations = 4.00 + 0.133 × 0 × 0.789 = 4.00 Professor Stock’s predicted course evaluations = 4.00 + 0.133 × 1 × 0.789 = 4.105
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