Question

Osteoporosis is a condition where bones become weak. It affects more than 200 million people worldwide. Exercise is one way to produce strong bones and to prevent osteoporosis. Since we use our dominant arm (the right arm for most people) more than our nondominant arm, we expect the bone in our dominant arm to be stronger than the bone in our nondominant arm. By comparing the strengths, we can get an idea of the effect that exercise can have on bone strength. Here are some data on the strength of bones, measured in cm4/1000cm4/1000, for the arms of 15 young men:

ID	Nondominant	Dominant
1	15.7	16.3
2	25	26.8
3	17.9	18.8
4	19	22
5	12.1	14.7
6	20.1	20
7	12.1	13.2
8	14.6	17.4
9	15.8	20
10	13.8	18.7
11	17.6	18.6
12	15.3	15.1
13	14.5	16.2
14	13.9	15
15	12.4	12.9

A young male who is not a baseball player has a bone strength of 16.0cm4/100016.0cm4/1000 in his nondominant arm. Predict the bone strength in the dominant arm for this person.

(Use decimal notation. Give your answer to three decimal places.)

Predicted bone strength is _____ cm^4/1000.

Answer 1

We will fit the linear regression model to the given data:

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	15.7	16.3	255.91	246.49	265.69
	25	26.8	670	625	718.24
	17.9	18.8	336.52	320.41	353.44
	19	22	418	361	484
	12.1	14.7	177.87	146.41	216.09
	20.1	20	402	404.01	400
	12.1	13.2	159.72	146.41	174.24
	14.6	17.4	254.04	213.16	302.76
	15.8	20	316	249.64	400
	13.8	18.7	258.06	190.44	349.69
	17.6	18.6	327.36	309.76	345.96
	15.3	15.1	231.03	234.09	228.01
	14.5	16.2	234.9	210.25	262.44
	13.9	15	208.5	193.21	225
	12.4	12.9	159.96	153.76	166.41
Sum =	239.8	265.7	4409.87	4004.04	4891.97

herefore, we find that the regression equation is:

When X=16 then

cm⁴/1000

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