A researcher develops a regression model to understand how student-to-teacher ratios affect test scores. The researcher theorizes that age, gender, and race do not impact test scores. However, a discussion with his colleagues reveals other factors could be important. As such, a second model is constructed. In this model, an additional explanatory variable reflecting the percent of classrooms with at least eight computers (PctComputer) is added.
The results are as follows:
TestScore = 698.9 - 2.28 STR
and
TestScore = 698.0 - 1.10 STR - 0.65 PctComputer
(1) Explain why you think the coefficient on the student-teacher ratio has changed so dramatically (been more than halved). Be very thorough and clearly explain important considerations.
(2) What potential problems exist in this analysis?
Show all work and calculations.