13.7 ▼ The authors of the paper “Weight-Bearing Activity during Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake” (Journal of Bone and Mineral Research [1994], 1089–1096) studied a number of variables they thought might be related to bone mineral density (BMD). The accompanying data on x 5 weight at age 13 and y 5 bone mineral density at age 27 are consistent with summary quantities for women given in the paper.
Weight (kg) BMD (g/cm2)
54.4 1.15 59.3 1.26 74.6 1.42 62.0 1.06 73.7 1.44 70.8 1.02 66.8 1.26 66.7 1.35 64.7 1.02 71.8 0.91 69.7 1.28 64.7 1.17 62.1 1.12 68.5 1.24 58.3 1.00 A simple linear regression model was used to describe the relationship between weight at age 13 and BMD at age 27. For this data:
a 5 0.558 b 5 0.009 n 5 15 SSTo 5 0.356 SSResid 5 0.313

a. What percentage of observed variation in BMD at age 27 can be explained by the simple linear regression model? (Hint: See Example 13.3.)

b. Give an estimate of s and interpret this estimate.

c. Give an estimate of the average change in BMD associated with a 1 kg increase in weight at age 13.

d. Compute an estimate of the mean BMD at age 27 for women whose age 13 weight was 60 kg.