ECON_6218_Solutions_to_Problem_Set_#1_Spring_2010

ECON_6218_Solutions_to_Problem_Set_#1_Spring_2010 - ECON...

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ECON 6218: ADVANCED BUSINESS AND ECONOMIC FORECASTING McGregor Spring 2010 Solutions to Problem Set #1 [1] A researcher has estimated the effects of gender on wages for a sample of 468 individuals. The results of one of the researcher’s regressions are shown below (with standard errors shown in parentheses): WAGES = 5.72 + 1.26 JobExperience – 0.92 FEMALE + 0.35 (JobExperience*FEMALE) (1.22) (0.31) (0.55) (0.20) WAGES are measured in dollars per hour; JobExperience is measured in years; and FEMALE is a dummy variable equal to one for females and zero for males. (a) Compute point estimates of the average “starting wages” for males and females. For males, the average starting wage is $5.72 per hour. For females, the average starting wage is $4.80 per hour. (b) Compute a 95% confidence interval for estimated starting wages for males. A 95% confidence interval for estimated starting wages for males is ( ) [] [ ] [ ] 11 . 8 $ , 33 . 3 $ 39 . 2 72 . 5 22 . 1 96 . 1 72 . 5 = ± = ± . (c) Test the null hypothesis that starting wages are unrelated to gender. We compute 673 . 1 55 . 0 92 . 0 = = t . Since 96 . 1 673 . 1 < , we fail to reject the null hypothesis that starting wages are unrelated to gender. (d) Test the null hypothesis that the effect of experience on wages is unrelated to gender. We compute 75 . 1 20 . 0 35 . 0 = = t . Since , we fail to reject the null hypothesis that the effect of experience on wages is unrelated to gender. 96 . 1 75 . 1 < (e) Sketch the relationships between wages and experience for males and females on the same graph. Briefly describe your findings. The results suggest that males have a higher average starting wage than females, while females’ wages increase more than males’ wages for each additional year of experience. 1
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Wages Female Males Experience [2] A researcher is studying the rationality of housing assessments. Data on assessments A and subsequent transactions price P were gathered on 88 houses and the following regression equation was estimated (with standard errors shown in parentheses): ln(P) = -14.47 + 0.976 ln(A) (16.27) (0.049) R 2 = 0.820 Residual Sum of Squares = 165,644.41 The researcher also calculated . Test the joint hypothesis that the assessments in the sample were rational (which requires that the intercept equal zero and the slope coefficient equal one). [] 99 . 448 , 209 ) ln( ) ln( 88 1 2 = = i A P We are testing the joint hypothesis that the intercept equals zero and the slope coefficient equals one. The appropriate test statistic is given by () () () [] k N q F k N RSS q RSS RSS UR UR R = , . In this problem, we have , 99 . 448 , 209 = R RSS 41 . 644 , 165 = UR RSS , 2 = q , and ( ) 86 = k N . The test statistic is () 37 . 11 926 , 1 902 , 21 86 41 . 644 , 165 2 41 . 644 , 165 99 . 448 , 209 = = . This test statistic follows an F distribution with 2 and 86 degrees of freedom.
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This note was uploaded on 01/27/2010 for the course ECON 6218 taught by Professor Mcgregor,r during the Spring '08 term at UNC Charlotte.

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ECON_6218_Solutions_to_Problem_Set_#1_Spring_2010 - ECON...

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