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Chapter 4: Q. 4.114 (page 182)

In Exercises 4.104 - 4.115, use the technology of your choice to perform the following tasks.

(a) Decide whether finding the regression line for the data is reasonable. If so, do parts (b) - (d).

(b) Obtain the coefficient of determination,

(c) Determine the percentage of variation in the observed values of the response variable explained by the regression and interpret your answer.

(d) State how useful the regression equation appears to be for making predictions.

In the paper 鈥淭otal Body Composition by Dual-Photon (153Gd) Absorptiometry鈥� (American Journal of Clinical Nutrition, Vol. 40, pp. 834鈥�839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured for percentage of body fat, using dual-photon absorptiometry. Each adult鈥檚 age and percentage of body fat are shown on the WeissStats CD.

Short Answer

Expert verified

(a) From the scatterplot, it is reasonable to find the regression line for the data since the observations are around the line.

(b) The coefficient of determination is 0.627.

(c) The percentage of variation in the observed values of the response variable explained by the regression is 62.7%.

(d)The regression equation is useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 62.7%which is greater than 50%.

Step by step solution

01

Part (a) Step 1. Given Information. 

Eighteen randomly selected adults were measured for percentage of body fat, using dual-photon absorptiometry.

02

Part (a) Step 2. The MINITAB procedure. 

The MINITAB procedure for constructing scatterplot is:

1. Choose Graph > Scatterplot.

2. Choose with Connect Line, click OK.

3. Under Y-variables, enter a column of %Fat and under X-variables enter a column of Age.

4. Click OK.

03

Part (a) Step 3. Graph the scatterplot. 

The MINITAB output is:

From the scatterplot, it is reasonable to find the regression line for the data since the observations are around the line.

04

Part (b) Step 1. The MINITAB procedure. 

The MINITAB procedure for finding the coefficient of determination is:

1. Choose Stat > Regression > Regression.

2. In response, enter the column %Fat.

3. In predictors, enter the column Age.

4. Click OK.

05

Part (b) Step 2. The MINITAB output 

The MINITAB output is:

From the MINITAB output, the coefficient of determination is0.627

06

Part (c) Step 1. Find the percentage of variation. 

From the MINITAB output, the percentage of variation in the observed values of the response variable explained by the regression is62.7%.

07

Part (d) Step 1. Explanation. 

The regression equation is useful for making predictions because the percentage of variation in the observed values of the response variable explained by the regression is 62.7%which is greater than50%.

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Most popular questions from this chapter

Regarding linear equations with one independent variable, answer the following questions:
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