Dropping a variable from a multiple linear regression model, causes another to become non-significant

Question

Suppose we have a regression model that measures college Grade Point Averages. The variables that we are using are hsize (the size of the graduating class in hundreds), hsize squared, sat (SAT Scores), female, and athlete.

After estimating for the model using STATA, athletes had a coefficient of .1693, with a T value of 4, and a P Value of 0.

If I remove SAT scores from the model, athletes coefficient changes to 0.00544 and its new p-value is a whopping .903 with a t value of 0.12.

What I'm asking is what could explain the change in the estimated effect of being an athlete in this model.

Basic question like this are almost always duplicates - How can adding a 2nd IV make the 1st IV significant? Also essentially duplicated here and here. That took approx 40 seconds. — Macro, Apr 03 '13 at 17:48

score 1 · Answer 1 · answered Apr 02 '13 at 23:54

It means that being an athlete is only an important predictor of GPA after controlling for SAT score.

What I would do to explicate this is make a scatter plot with SAT on the X axis, GPA on the Y axis, and different color dots for athletes and non-athletes. Then I'd smoothed lines to each set of dots.

Dropping a variable from a multiple linear regression model, causes another to become non-significant

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