Suppose you estimate the sample regression function $$ Midt\widehat {erm ~Sc}ore = 62.33 + 4.62 \cdot \text { Time Taken } - 0.038 \cdot \text { Time Taken } { } ^ { 2 }$$
You should conclude that the marginal effect of time taken on midterm score is _____ for a student going from 48 minutes to 49 minutes to complete the exam.
A)0.972
B)4.582
C)4.62
D)221.76

Question

Suppose you estimate the sample regression function $$  Midt\widehat {erm ~Sc}ore = 62.33 + 4.62 \cdot \text { Time Taken } - 0.038 \cdot \text { Time Taken } { } ^ { 2 }$$
You should conclude that the marginal effect of time taken on midterm score is _____ for a student going from 48 minutes to 49 minutes to complete the exam.
A)0.972
B)4.582
C)4.62
D)221.76

Quizplus · Accepted Answer

The marginal effect of time taken on midterm score, when going from 48 minutes to 49 minutes, is calculated by taking the derivative of the given regression function with respect to Time Taken and then evaluating it at Time Taken = 48. The derivative of the regression function with respect to Time Taken is $4.62 - 2 \cdot 0.038 \cdot \text{Time Taken}$. Substituting Time Taken = 48 gives $4.62 - 2 \cdot 0.038 \cdot 48 = 4.62 - 3.648 = 0.972$.

Suppose You Estimate the Sample Regression Function Midterm Sc^ore=62.33+4.62⋅ Time Taken −0.038⋅ Time Taken 2 Midt\widehat {erm ~Sc}ore = 62.33 + 4.62 \cdot \text { Time Taken } - 0.038 \cdot \text { Time Taken } { } ^ { 2 }Midterm Score=62.33+4.62⋅ Time Taken −0.038⋅ Time Taken 2

Suppose You Estimate the Sample Regression Function $Midt\widehat {erm ~Sc}ore = 62.33 + 4.62 \cdot \text { Time Taken } - 0.038 \cdot \text { Time Taken } { } ^ { 2 }$