The following scatterplot shows productivity and number hired workers with a fitted quadratic regression model. Assuming that the values of Hires can be nonintegers, what is the maximum value of Productivity predicted by the model?
A) 29.58
B) 124.603
C) 35.086
D) 127.50

Question

The following scatterplot shows productivity and number hired workers with a fitted quadratic regression model.  Assuming that the values of Hires can be nonintegers, what is the maximum value of Productivity predicted by the model?
A) 29.58 
B) 124.603 
C) 35.086 
D) 127.50

Quizplus · Accepted Answer

From the quadratic regression model, we can see that the maximum value of productivity occurs at the vertex of the parabolic curve. The vertex can be found by taking the negative coefficient of the quadratic term (-0.2838) and dividing it by twice the coefficient of the linear term (0.5639 * 2). This gives us the value of 0.2518. We can then substitute this value into the quadratic regression model to find the corresponding predicted value of productivity:

Predicted Productivity = 43.901 + 64.164(0.2518) - 24.971(0.2518)^2 
Predicted Productivity = 124.603

Therefore, the maximum predicted value of productivity is 124.603.

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