Chapter 8 Answers - Chapter 8 Answers 2(a According to the...

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Chapter 8 Answers 2. (a) According to the regression results in column (1), the house price is expected to increase by 21% ( = 100% × 0.00042 × 500 ) with an additional 500 square feet and other factors held constant. The 95% confidence interval for the percentage change is 100% × 500 × (0.00042 ± 1.96 × 0.000038) = [17.276% to 24.724%]. (b)Because the regressions in columns (1) and (2) have the same dependent variable, 2 R can be used to compare the fit of these two regressions. The log-log regression in column (2) has the higher 2 , R so it is better so use ln( Size ) to explain house prices. (c)The house price is expected to increase by 7.1% ( = 100% × 0.071 × 1). The 95% confidence interval for this effect is 100% × (0.071 ± 1.96 × 0.034) = [0.436% to 13.764%]. (d)The house price is expected to increase by 0.36% (100% × 0.0036 × 1 = 0.36%) with an additional bedroom while other factors are held constant. The effect is not statistically significant at a 5% significance level: = = < 0.0036 0.037 | | 0.09730 1.96. t Note that this coefficient measures the effect of an additional bedroom holding the size of the house constant. (e)The quadratic term ln( Size ) 2 is not important. The coefficient estimate is not statistically significant at a 5% significance level: = = < 0.0078 0.14 | | 0.05571 1.96. t (f) The house price is expected to increase by 7.1% ( = 100% × 0.071 × 1) when a swimming pool is added to a house without a view and other factors are held constant. The house price is expected to increase by 7.32% ( = 100% × (0.071 × 1 + 0.0022 × 1) ) when a swimming pool is added to a house with a view and other factors are held constant. The difference in the expected percentage change in price is 0.22%. The difference is not statistically significant at a 5% significance level: = = < 0.0022 0.10 | | 0.022 1.96. t 3 (a) The regression functions for hypothetical values of the regression coefficients that are consistent with the educator’s statement are: 1 0 β and 2 0. β < When TestScore is plotted against STR the regression will show three horizontal segments. The first segment will be for values of STR 20; < the next segment for 20 25; 0 STR the final segment for 25. STR The first segment will be higher than the second, and the second segment will be higher than the third. (b)It happens because of perfect multicollinearity. With all three class size binary variables included in the regression, it is impossible to compute the OLS estimates because the intercept is a perfect linear function of the three class size regressors. 4. (a) With 2 years of experience, the man’s expected AHE is 2 ln( ) (0.0899 16) (0.521 0) (0.0207 0 16) (0.232 2) 0.000368 2 ) (0.058 0) (0.078 0) (0.030 1) 1.215 2.578 = × - × + × × + × - × - × - × - × + = AHE With 3 years of experience, the man’s expected AHE is 2 ln( ) (0.0899 16) (0.521 0) (0.0207 0 16) (0.232 3) (0.000368 3 ) (0.058 0) (0.078 0) (0.030 1) 1.215 2.600 = × - × + × × + × - × - × - × - × + = AHE Difference = 2.600 - 2.578 = 0.022 (or 2.2%) (b)With 10 years of experience, the man’s expected AHE is 2 ln( ) (0.0899 16) (0.521 0) (0.0207 0 16) (0.232 10) (0.000368 10 ) (0.058 0) (0.078 0) (0.030 1) 1.215 2.729 = × - × + × × + × - × - × - × - × + = AHE With 11 years of experience, the man’s expected AHE is
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2 ln( ) (0.0899 16) (0.521 0) (0.0207 0 16) (0.232 11) (0.000368 11 ) (0.058 0) (0.078 0) (0.030 1) 1.215 2.744 = × - × + × × + × - × - × - × - × + = AHE Difference = 2.744 - 2.729 = 0.015 (or 1.5%) (c)The regression in nonlinear in experience (it includes Potential experience 2 ).
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