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^* + β₁Hours 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* 0, then β₁* 0

Question

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^* + β₁Hours 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

Quizplus · Accepted Answer

If β₁₂* > 0, indicating a positive relationship between Major GPA and exam grades, it suggests that part of the effect previously attributed to hours studied (in the simple regression without GPA) may actually be due to the higher GPA of those who studied more. Thus, when GPA is controlled for, the estimated effect of hours studied (β₁₁*) on exam grades is likely to be smaller than the initial estimate (b₁₁), because some of the effect initially attributed to studying more may actually be due to having a higher GPA.

Suppose You Have Many Observations of the Scores Students Got