The estimate regression equation for the average cost of widgets is: ^Widgets = 7.33 - 0.2340 Output + 0.1892 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 $0.71 decrease in predictive average cost. D) The increase in output units results in a $0.71 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 = 7.33 - 0.2340(Output) + 0.1892(Output)^2. For 2 million units, the predicted cost is 7.33 - 0.2340(2) + 0.1892(2)^2 = 7.33 - 0.468 + 0.7568 = 7.6188. For 3 million units, it is 7.33 - 0.2340(3) + 0.1892(3)^2 = 7.33 - 0.702 + 1.7108 = 8.3388. The difference, or the increase, is 8.3388 - 7.6188 = 0.72, which, when rounded, indicates a $0.71 increase in predictive average cost.

The Estimate Regression Equation for the Average Cost of Widgets