The following scatterplot shows productivity and number hired workers with a fitted quadratic regression model. Assuming that the number of hired workers must be integer, how many workers should be hired to achieve the highest productivity according to the model?
A) 26
B) 28
C) 30
D) 32

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 integer, how many workers should be hired to achieve the highest productivity according to the model?
A) 26 
B) 28 
C) 30 
D) 32

Quizplus · Accepted Answer

In the quadratic regression model, the highest point of the parabola represents the maximum productivity. According to the scatterplot, the highest point is approximately at the productivity level of 92. To find the corresponding number of workers, we need to look at the vertex of the parabola. The vertex of a quadratic function in the form of y = ax^2 + bx + c is at x = -b/2a. In our case, the model is productivity = -0.65(worker)^2 + 44.4(worker) + 56.6. So the vertex is at worker = -44.4/(2*(-0.65)) = 34.15, which is between 34 and 35 workers. Since we can only hire a whole number of workers, we need to choose the closest integer to the vertex, which is 30 workers. Therefore, the answer is C.

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