Question

The authors of the paper "Weight-Bearing Activity during Youth Is a More Important Factor for Peak Bone Mass than Calcium Intake" studied a number of variables they thought might be related to bone mineral density (BMD). The accompanying data on

x = weight

at age 13 and

y = 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. The following values are given for this data.

a = 0.558           b = 0.009         n = 15
SSTo = 0.356     SSResid = 0.313

(a)

What percentage of observed variation in BMD at age 27 can be explained by the simple linear regression model? (Round your answer to one decimal place.)

%

(b)

Give an estimate of σ. (Round your answer to three decimal places.)

Interpret this estimate.

This is an average of bone mineral density values in the sample from the value predicted by the least-squares line.This is a typical deviation of a weight value in the sample from the value predicted by the least-squares line.    This is an average of weight values in the sample from the value predicted by the least-squares line.This is a typical deviation of a bone mineral density value in the sample from the value predicted by the least-squares line.

(c)

Give an estimate of the average change in BMD associated with a 1 kg increase in weight at age 13. (Round your answer to three decimal places.)

g/cm²

(d)

Compute an estimate of the mean BMD at age 27 for women whose weight at age 13 was 55 kg. (Round your answer to three decimal places.)

g/cm²

Answer 1