Wages, class, and gender

Topic: Linear model examples · more questions on this topic
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A linear model for yearly wages, in thousands of dollars, uses social class and gender. The intercept, for upper-class men, is 93.242. The working-class coefficient is -4.247. The coefficient on the indicator for women is 3.927, with t statistic corresponding to p-value 0.01029 on the gender row. The gender sum of squares in the analysis of variance is 3194 on 1 degree of freedom, and the residual mean square is 102.

  1. Estimate the expected wage of a working-class man.

  2. What does the coefficient 3.927 mean?

  3. Does the fit indicate that women earn more than men, on average, after class is accounted for?

  1. A working-class man is estimated at 93.242-4.247=88.995, about 89 thousand dollars.

  2. The coefficient 3.927 is the estimated difference, in thousands of dollars, between women and men of the same class. The sign says women are estimated higher.

  3. The gender row has p-value 0.01029, so the difference is distinguishable from zero at level 0.05. The gender mean square is 3194/1 and the residual mean square is 102, so F=3194/102=31.3, which is the square of the t statistic and gives the same conclusion.