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) o 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) o 2 x 2 to the data Is there evidence that ni...

a To fit the model Ey o 1x1 to the data one would need to use linear regression to estimate the coef ...

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

Question:

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 + 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) = β_o + 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) = β_o + 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 = β̂_o + β̂₁x₁ + β̂₂x₂ + .... β̂_kx_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).