Refer to Muscle mass Problem 1.27.
a. Fit a two-region regression tree. What is the first split point based on age? What is SSE for this two-region tree?
b. Find the second split point given the two region tree in part (a). What is SSE for the resulting three-region tree?
c. Find the third split point given the three-region tree in part (b). What is SSE for the resulting four-region tree?
d. Prepare a scatter plot of the data with the four-region tree in part (c) superimposed. How well does the tree fit the data? What does the tree suggest about the change in muscle mass with age?
e. Prepare a residual plot of 
versus Yi for the four-region tree in part (d). State your findings.
Problem 1.27
Muscle mass. A person's muscle mass is expected to decrease with age. To explore this relationship in women, a nutritionist randomly selected 15 women from each lO-year age group, beginning with age 40 and ending with age 79. The results follow; X is age, and Y is a measure of muscle mass. Assume that first-order regression model (1.1) is appropriate.
a. Obtain the estimated regression function. Plot the estimated regression function and the data. Does a linear regression function appear to give a good fit here? Does your plot support the anticipation that muscle mass decreases with age?
b. Obtain the following: (1) a point estimate of the difference in the mean muscle mass for women differing in age by one year, (2) a point estimate of the mean muscle mass for women aged X = 60 years, (3) the value of the residual for the eighth case, (4) a point estimate of σ2.