Refer to Exercise 10 in Section 7.4.
a. Divide the data into two groups: points where R1 < 4 in one group, points where R1 ≥ 4 in the other. Compute the least-squares line for predicting R2 from R1 for each group. (You already did this if you did Exercise 10c in Section 7.4.)
b. For one of the two groups, the relationship is clearly nonlinear. For this group, fit a quadratic model (i.e., using R1 and R21 as independent variables), a cubic model, and a quartic model. Compute the P-values for each of the coefficients in each of the models.
c. Plot the residuals versus the fitted values for each of the three models in part (b).
d. Compute the correlation coefficient between R31 and R41, and make a scatterplot of the points (R31, R41).
e. On the basis of the correlation coefficient and the scatterplot, explain why the P-values are much different for the quartic model than for the cubic model.
f. Which of the three models in part (b) is most appropriate? Why?