The following scatterplot shows productivity and number hired workers with a fitted quadratic regression model. Assuming that the number of hired workers must be an integer, what is the maximum productivity predicted by the model?
A) 29.58
B) 30.00
C) 124.603
D) 124.585

Question

The following scatterplot shows productivity and number hired workers with a fitted quadratic regression model.  Assuming that the number of hired workers must be an integer, what is the maximum productivity predicted by the model?
A) 29.58 
B) 30.00 
C) 124.603 
D) 124.585

Quizplus · Accepted Answer

The maximum productivity predicted by the model is the maximum point of the quadratic curve. From the scatterplot, it appears that the maximum point is between 125 and 130 on the x-axis (number of hired workers). To determine the exact point, we can calculate the vertex of the quadratic equation. The equation given in the plot is:

Productivity = -0.2672($Hired~workers$)$^2$ + 41.9456($Hired~workers$) - 538.4764

The vertex of this quadratic equation is:

$Hired~workers$ = -b/2a = -41.9456/(2(-0.2672)) ≈ 78.4

To get the maximum productivity, we plug this value of $Hired~workers$ into the equation:

Productivity = -0.2672(78.4)$^2$ + 41.9456(78.4) - 538.4764 ≈ 124.585

Therefore, the maximum predicted productivity is approximately 124.585, which corresponds to choice (D).

The Following Scatterplot Shows Productivity and Number Hired Workers with a Fitted