7 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  b0  b1X  b2X2  b3X3  

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):

yˆ  29.7  19.8X  0.39X2  0.005X3

(0.78) (0.62) (1.25)

a For a  0.10, test H0: bi  0 against Ha: bi  0

(i  1, 2, 3).

b Determine R2 for this model. How can the high R2 value be reconciled with the answer to part (a)?