Changing coefficient when an independent variable is added?

[Tim 1234]

Homework Statement

(b) (10 points) Estimate the equation income = β0 + β1female. Interpret theβ1 coefficient. How does β1 compare to your difference in means in part a?
(c) (10 points) Estimate income as a linear function of highest grade and female. Report results. How does the coefficient on female change?
(d) (10 points) How could we use the regression results in (b) and (c) to tell if women have higher average education than men?

2. Homework Equations
b) income = 39331.2-13506.8female
c)income = -14676.4+3896.5highest_grade-15487.9female
The coefficient on female decreased by 1981.10 with the inclusion of highest grade completed.

The Attempt at a Solution

I know from the data set that women do have a higher average education than men.
Obviously adding the new variable increased the amount by which income is decreased if the individual is a female, but I don't really understand why that indicates a higher average education for women than for men.

 

[mighty2000]

The coefficient on female in part b represents the difference in average income between men and women, assuming all other variables are held constant. This means that on average, women in this data set earn $13,506.80 less than men. This difference in means is a simple comparison of the average income for men and women, while the coefficient in the regression equation takes into account other factors that may influence income, such as education and experience.

In part c, the coefficient on female changes to -15,487.90, which means that on average, women earn $15,487.90 less than men with the same highest grade completed. This suggests that education is an important factor in explaining the income difference between men and women. By including education in the regression equation, we can better understand the relationship between education and income, and how it may differ for men and women.

To determine if women have a higher average education than men, we can compare the coefficients on female in part b and part c. If the coefficient is larger in part c, it suggests that women have a higher average education than men, as education is a significant factor in determining income. In this case, the coefficient on female did increase, indicating that women may have a higher average education than men in this data set. However, further analysis would be needed to confirm this conclusion.