Suppose You Have Many Observations of the Scores Students Got

Multiple Choice

Suppose you have many observations of the scores students got on an exam, with other characteristics of the students including how many hours they studied for the exam that week and what is their current major GPA. Now, suppose you ran the standard linear regression of the exam grade on the number of hours studied: Grade_i = β₀ + β₁ Hours Studied_i + U_i and got an estimate of β₁, call it b₁. Now, suppose a colleague tells you that the students with above average GPAs were the students who studied more for the exam. How does your estimate of β₂* in the following regression, Grade_i = β₀^* + β₁ Hours Studied_i + β₂^* Major GPA_i + U_i, inform you of what your estimate of what β₁^* will be for that same regression?

A) If β₂* > 0, then β₁* > b₁
B) If β₂* > 0, then β₁* < b₁
C) If β₂* < 0, then β₁* > 0
D) If β₂* > 0, then β₁* > 0