Stats 110B, Spring 99 Quiz 7

Name:
 
 

Once again, consider the salaries of 52 faculty from some northwestern college. Someone believes that not only do men start out making more money than women there, but the menís salaries climb faster with experience, too.
 
 

  1. Write a linear model to test this. Let y represent salary, x1 years at the college, and x2 = 1 if female, 0 if male.

    2.  

     

    y = beta0 + beta1 * (x2) + beta2*x1 + beta3*(x1*x2)

    If you are male,then x2=0 and your intercept is beta0 and your slope is beta2.  If you are female, then x2=1 and your intercept is beta0+beta1 and your slope is beta2+beta3
     
     

  2. Below is output from one such linear model. Interpret it with respect to answering this personís theory. "Year" is years at the college, "Sex" is a 1 if female, 0 if male. "yeargender" is Sex*Year. (Even though no p-values are given, take a good guess at whether the coefficients are significant or not)
Response = Salary

Terms = (yeargender Year Sex)

Coefficient Estimates

Label Estimate Std. Error t-value

Constant 18222.6 1159.01 15.723

yeargender -277.228 362.609 -0.765

Year 741.024 111.799 6.628

Sex 102.725 2042.43 0.050

R Squared: 0.559673

Sigma hat: 3845.89

Number of cases: 52

Number of cases used: 51

Degrees of freedom: 47
 

This is the model given in Part 1.  If we believed that all of the terms were significant, then it says that men make, as an average starting salary,
18222.6, and women make, on average, 102.72 more (as a starting salary-- that is, when Year=0).  But then the men's slope is 741, which means for each additional year of experience they are making 741 dollars more, on average.  But women, on the other hand, are making less by  741-277 per year.

However, the t-statistics for yeargender and sex are so small, that if we were to test for a relationship on sex, yeargender and year being held constant, we would find it insignificant. And the same can be said for yeargender holding sex and year constant.  If we could, we should take sex out of the model and recompute.
Most likely we'll find that there is no difference due to gender, and that men and women have the same slope and intercept.