# Changing coefficient when an independent variable is added?

1. Sep 28, 2016

### Tim 1234

1. The problem statement, all variables and given/known data
(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. Relevant equations

b) income = 39331.2-13506.8female
The coefficient on female decreased by 1981.10 with the inclusion of highest grade completed.

3. 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.

2. Oct 3, 2016