# We have been assigned to determine how the total weekly production cost for Widgetco depends on the…

We have been assigned to determine how the total weekly production cost for Widgetco depends on the number of widgets produced during the week. The following model has been proposed:

Y = β_{0} + β_{1}X + β_{2}X^{2} + β_{3}X^{3} + ε

where X = number of widgets produced during the week and Y = total production cost for the week. For 15 weeks of data, we found that SSR = 215,475 and SST = 229,228. For this model, we obtain the following estimated regression equation (t-statistics for each coefficient are in parentheses):

a For α = 0.10, test H_{0}: β_{i} = 0 against H_{a}: β_{i} ≠ 0 (i = 1, 2, 3).

b Determine R^{2} for this model. How can the high R^{2} value be reconciled with the answer to part (a)?