Following are the results of estimating a multiple linear regression model where
ID: 3311289 • Letter: F
Question
Following are the results of estimating a multiple linear regression model where the dependent variable represents tenure-track CMU faculty members' salaries in 2004-05 and the independent variables are: female: a dummy variable; 1 = female, 0 = male years CMU: the number of years that the faculty member has been employed by CMU. CBA: a dummy variable; 1 = faculty merm ber in the College of Business Administration, 0-otherwise CCFA: a dummy variable; 1 = faculty member in the College of Communications and Fine Arts, 0 : otherwise. Use the regression results below to answer questions 1-10 SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.689304 0.475141 0.471819 13502.68 637 df MS 1.04E+11 26078135375 143.0330479 5.16359E-87 Regression Residual Total 632 1.15E+11 1823224476 636 2.2E+11 Standard nCoefficients t Stat Error 1022.08 58.24773234 2.923E-256 59533.8 -654.15) 1154.728-5664665589 (2.2386E08- 805.2356 51.35222 15.68063719 4.75047E-47 4211.21 1577.055267030207 0.007773242 Intercept female CMU CBA 19727.06 1650.43 11.95268028 787894E-30Explanation / Answer
5.
The adjusted R squared tells that 47.18% of variation is explained by only the independent variables that actually affect the dependent variable.
6.
F-Statistic measure the significance of the model. It measures that whether there is linear relation between independent and dependent variables.
7.
Null Hypothesis H0: Salaries are independent of gender, number of years in CMU, whether faculty member in CBA and CCFA. Model is not significant.
Alternative Hypothesis Ha: Salaries are dependent of atleast one of the following factors - gender, number of years in CMU, whether faculty member in CBA and CCFA. Model is significant.
8.
As, P-value of F is near 0 and is less than the significance level of 0.01, we reject the null hypothesis and conclude that the model is significant.
9.
As, the coeffiecient of female is negative (-6541.15), women faculty members do not earn as much as men.
The standard error of female coeffcient is 1154.728
t statistic = -6541.15 / 1154.728 = -5.665
For degree of freedom = 632, P(t > -5.665) is near 1.
So, we are almost 100% confident that women faculty members do not earn as much as men.
10.
Salary = 59533.87 - 6541.15 female + 805.2356 years in CMU + 19727.06 CBA - 4211.21 CCFA
= 59533.87 - 6541.15 * 1 + 805.2356 * 10 + 19727.06 * 0 - 4211.21 * 1
= 56833.87