The estimate regression equation for the average cost of widgets is: ^Widgets = 7.23 - 0.2478 Output + 0.1954 Output². Both predictor variables are statistically significant at 5% level, confirming the quadratic effect. What is the predictive average from an output level of 2 million units to 3 million units? A) The increase in output units results in a $0.02 decrease in predictive average cost. B) The increase in output units results in a $0.24 increase in predictive average cost. C) The increase in output units results in a $0.73 decrease in predictive average cost. D) The increase in output units results in a $0.73 increase in predictive average cost.

Question

Quizplus · Accepted Answer

To calculate the change in predictive average cost from an output level of 2 million units to 3 million units, we first calculate the predicted cost for both levels and then find the difference. The regression equation is given as ^Widgets = 7.23 - 0.2478(Output) + 0.1954(Output^2). For 2 million units (Output = 2), the predicted cost is 7.23 - 0.2478(2) + 0.1954(2^2) = 7.23 - 0.4956 + 0.7816 = 7.516. For 3 million units (Output = 3), the predicted cost is 7.23 - 0.2478(3) + 0.1954(3^2) = 7.23 - 0.7434 + 1.7586 = 8.2452. The difference, or the increase, in predictive average cost from 2 million to 3 million units is 8.2452 - 7.516 = 0.7292, which rounds to $0.73, indicating an increase in predictive average cost.

The Estimate Regression Equation for the Average Cost of Widgets