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 reaches its maximum at _____ minutes taken.
A)62.33
B)60.79
C)121.58
D)4.582

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 reaches its maximum at _____ minutes taken.
A)62.33
B)60.79
C)121.58
D)4.582

Quizplus · Accepted Answer

To find the point of maximum marginal effect, we need to take the derivative of the regression function with respect to time taken and set it equal to 0:

$$ \frac{d}{dt} (62.33 + 4.62t - 0.038t^2) = 4.62 - 0.076t = 0 $$

Solving for t, we get t = 60.79. Therefore, the point of maximum marginal effect is at 60.79 minutes taken.

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 $Midt\widehat {erm ~Sc}ore = 62.33 + 4.62 \cdot \text { Time Taken } - 0.038 \cdot \text { Time Taken } { } ^ { 2 }$