Unformatted text preview: Homework 4 5.4 a) -3.13+1.4716=20.39 b) -3.13+1.4714-(-3.13+1.4712)=1.472=2.94 c) Assuming college would entail four additional years of education, this would raise expected earnings by 1.474=5.88<10. The standard deviation of our estimate of is .07. This makes the upper bound of the 95% confidence interval 1.61, so that the upper bound of the confidence interval for four years of education would be 1.614=6.44. This is still less than 10. 5.9 a) Recall that a linear function of , then we get the proposed estimator. Therefore , ,..., takes the form is a linear function of . Note that if we let , ,..., . b) | , , ,..., ,..., , ,..., | , ,..., | , ,..., | , ,..., 5.15
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, , , 6.6 a) There are many variables that are correlated with both the explanatory variable (per capita size of the county's police force) and the error term. We might want to add variables such as population density and unemployment rate. b) The variables above would correlate positively with both per capita police force and the error term in the regression. Therefore the X term would be positive, making 2 2 0 . 6.11 a) b) c) ; 0 2 = ; 0 0 d) = 1 e) )= 2 0 - 0 E5.3 a) b) c) d) e) Yes, it is statistically significant at all the suggested significance levels. The p-value is 0.000. The 95% confidence interval would be [-.1003,-.0464]. For females, the 95% confidence interval would be [-.1010,-.0273]. For males, the 95% confidence interval would be [-.1234,-.0443] No, the distance is not statistically significant. This can be seen either by noting the 95% confidence intervals overlap or doing a t-test on the difference, using the square root of the sum of the variances of the slope estimates as the standard deviation. E6.2 a) -.073. b) -.032. c) Yes, it is, and yes, it does seem that the regression in a) suffers from important omitted variable bias. d) The adjusted R-squared in b) is much higher than the R-squared in a). The adjusted R-squared is close to the R-squared in b) because the number of observations is large relative to the number of explanatory variables. e) The effect of an individual's father having attended college on their years of completed schooling. f) The county unemployment rate and the state hourly manufacturing wage are both correlated with distance from the nearest college as well as years of completed schooling. A high unemployment rate means that a decent job would be hard to find without a good education. Likewise, high wages in manufacturing, a sector that often doesn't require as many years of schooling, would decrease the relative benefit of years of schooling, and therefore decrease the average years of schooling in the population. As we would expect, the unemployment coefficient is positive, and the manufacturing wage coefficient is negative. g) Bob's predicted years of completed schooling = 8.828 - .0315*2 + .0938*58 + .3951 + .1521 + .3680 + .0232*7.5 -.0518*9.75 = 14.80. h) Jim's predicted years of completed schooling = Bob's predicted years - .0315*2 (since he is twenty miles farther from nearest college) = 14.73 ...
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