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) = β_{o} + β_{1}x_{1} to the data. Is there evidence that tar content (x_{1}) is useful for predicting carbon monoxide content (y)?

b. Fit the model E(y) = β_{o} + β_{2}x_{2} to the data. Is there evidence that nicotine content (x2) is useful for predicting carbon monoxide content (y)?

c. Fit the model E(y) = β_{o} + β_{3}x_{3} to the data. Is there evidence that weight (x3) is useful for predicting carbon monoxide content (y)?

d. Compare the signs of β̂_{1}, β̂_{2}, and β̂_{3} 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 = β̂_{o} + β̂_{1}x_{1} + β̂_{2}x_{2} + .... β̂_{k}x_{k}. 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).