Refer to the FTC cigarette data of Example 11.14. Recall that the

Refer to the FTC cigarette data of Example 11.14. Recall that the data are saved in the FTC2 file.

a. Fit the model E(y) = βo + β1x1 to the data. Is there evidence that tar content (x1) is useful for predicting carbon monoxide content (y)?

b. Fit the model E(y) = βo + β2x2 to the data. Is there evidence that nicotine content (x2) is useful for predicting carbon monoxide content (y)?

c. Fit the model E(y) = βo + β3x3 to the data. Is there evidence that weight (x3) is useful for predicting carbon monoxide content (y)?

d. Compare the signs of β̂1, β̂2, and β̂3 in the models of parts a, b, and c, respectively, to the signs of the β̂ ’s in the multiple regression model fit in Example 11.14. The fact that the ’s change dramatically when the independent variables are removed from the model is another indication of a serious multicollinearity problem.


Data from Exercise 11.14

Let l = ŷ = β̂o + β̂1x1 + β̂2x2 + .... β̂kxk. Use the T statistic of Exercise 11.13, in conjunction with the pivotal method, to derive the formula for a (1 - α)100% confidence interval for E(y).