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Unformatted text preview: Chapter 8 Nonlinear Regression Functions Solutions to Exercises 3 (a) The regression functions for hypothetical values of the regression coefficients that are consistent with the educator’s statement are: 1 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; ≤ ≤ 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 · 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 ). (d)Yes, the coefficient on Potential experience 2 is significant at the 1% level. (e) No. This would affect the level of ln( AHE ), but not the change associated with another year of experience. (f) Include interaction terms Female × Potential experience and Female × ( Potential experience ) 2 . 6. (a) (i) There are several ways to do this. Here is one. Create an indicator variable, say DV 1, that equals one if %Eligible is greater than 20% and less than 50%. Create another indicator, say DV 2, that equals one if %Eligible is greater than 50%. Run the regression: = + + × + × + 1 2 3 % 1 % 2 % other regressors TestScore Eligible DV Eligible DV Eligible β β β β The coefficient β 1 shows the marginal effect of %Eligible on TestScores for values of %Eligible 20%, β 1 + β 2 shows the marginal effect for values of %Eligible between 20% and 50% and β 1 + β 3 shows the marginal effect for values of %Eligible greater than 50%....
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This note was uploaded on 02/15/2010 for the course ECONOMICS NRFS10 taught by Professor Unknown during the Spring '10 term at Rutgers.
 Spring '10
 Unknown

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