Osteoporosis is a condition where bones become weak. It affects more than 200 mi

ID: 3206937 • Letter: O

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:

The least-squares regression line for these data is

dominant=2.523+0.947 nondominantdominant=2.523+0.947 nondominant.

Calculate the residuals for first four cases.

Residual is actual value minus predicted value.

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

Residual for case 1 is_____ cm4/1000.

Residual for case 2 is______ cm4/1000.

Residual for case 3 is______ cm4/1000.

Residual for case 4 is______ cm4/1000.

ID Nondominant Dominant 1 15.9 16.3 2 25 26.8 3 18.1 18.9 4 19.2 22.1 5 12 14.6 6 20.1 20 7 12.2 12.9 8 14.5 17.3 9 15.9 19.9 10 13.7 18.9 11 17.7 18.8 12 15.7 15.2 13 14.2 16.2 14 14.1 14.9 15 12.3 12.9

Explanation / Answer

Solution:

Here, we have to find the residuals for the first four observations.

We are given a regression equation as below:

Dominant = 2.523+0.947*non-dominant

We have to find the predicted dominant values by using above regression equation.

Dominant = 2.523+0.947*15.9 = 17.581

Dominant = 2.523+0.947*25 = 26.198

Dominant = 2.523+0.947*18.1 = 19.664

Dominant = 2.523+0.947*19.2 = 20.706

Residual = Observed value – Predicted value

Residual = 16.3 - 17.581 = -1.281

Residual = 26.8 - 26.198 = 0.602

Residual = 18.9 - 19.664= -0.764

Residual = 22.1 - 20.706 = 1.394

Observation

Non-dominant

Dominant

Predicted Dominant

Residuals

15.9

16.3

17.581

-1.281

26.8

26.198

0.602

18.1

18.9

19.664

-0.764

19.2

22.1

20.706

1.394