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Chapter 10: Q7BSC (page 468)

In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to the

StatCrunch display and answer the given questions or identify the indicated items.

The display is based on Data Set 5 “Family Heights” in Appendix B.

Should the multiple regression equation be used for predicting the height of a son based on the height of his father and mother? Why or why not?

Short Answer

Expert verified

The multiple regression equation cannot be used for predicting the height of a son based on the heights of his father and mother as the measure of R-squared values is low, which suggests poor fit.

Step by step solution

01

Given information

An output for regression is known.

02

Analyze the regression output

Compare each measure with the provided output.

  • TheP-valuein the last columnof theanalysis of variance table for the multiple regression model is low. It is less than 0.0001, which suggests that the model is overall significant.
  • Each variable is significant as the P-values are less than 0.05.
  • The value of the coefficient of determination (0.3249) and the adjusted value of the coefficient of determination (0.3552) are not high, which indicates a poor fit.

Therefore,the multiple regression equation fits the sample data, but it is not a good fit.

Thus, it should not be used for predicting the height of a son based on the heights of his father and mother.

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Most popular questions from this chapter

Critical Thinking: Is the pain medicine Duragesic effective in reducing pain? Listed below are measures of pain intensity before and after using the drug Duragesic (fentanyl) (based on data from Janssen Pharmaceutical Products, L.P.). The data are listed in order by row, and corresponding measures are from the same subject before and after treatment. For example, the first subject had a measure of 1.2 before treatment and a measure of 0.4 after treatment. Each pair of measurements is from one subject, and the intensity of pain was measured using the standard visual analog score. A higher score corresponds to higher pain intensity.

Pain Intensity Before Duragesic Treatment

1.2

1.3

1.5

1.6

8

3.4

3.5

2.8

2.6

2.2

3

7.1

2.3

2.1

3.4

6.4

5

4.2

2.8

3.9

5.2

6.9

6.9

5

5.5

6

5.5

8.6

9.4

10

7.6










Pain Intensity After Duragesic Treatment

0.4

1.4

1.8

2.9

6

1.4

0.7

3.9

0.9

1.8

0.9

9.3

8

6.8

2.3

0.4

0.7

1.2

4.5

2

1.6

2

2

6.8

6.6

4.1

4.6

2.9

5.4

4.8

4.1










Matched Pairs The methods of Section 9-3 can be used to test a claim about matched data. Identify the specific claim that the treatment is effective, then use the methods of Section 9-3 to test that claim.

Confidence Intervals for a Regression Coefficients A confidence interval for the regression coefficient b1 is expressed

\(\begin{array}{l}{b_1} - E < {\beta _1} < {b_1} + E\\\end{array}\)

Where

\(E = {t_{\frac{\alpha }{2}}}{s_{{b_1}}}\)

The critical t score is found using n –(k+1) degrees of freedom, where k, n, and sb1 are described in Exercise 17. Using the sample data from Example 1, n = 153 and k = 2, so df = 150 and the critical t scores are \( \pm \)1.976 for a 95% confidence level. Use the sample data for Example 1, the Stat diskdisplay in Example 1 on page 513, and the Stat Crunchdisplay in Exercise 17 to construct 95% confidence interval estimates of \({\beta _1}\) (the coefficient for the variable representing height) and\({\beta _2}\) (the coefficient for the variable representing waist circumference). Does either confidence interval include 0, suggesting that the variable be eliminated from the regression equation?

Interpreting r. In Exercises 5–8, use a significance level of A = 0.05 and refer to the accompanying displays.

5. Bear Weight and Chest Size Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in Data Set 9 “Bear Measurements” in Appendix B; results are shown in the accompanying Statdisk display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight?

Interpreting the Coefficient of Determination. In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Weight , Waist r = 0.885 (x = weight of male, y = waist size of male)

In Exercises 5–8, we want to consider the correlation between heights of fathers and mothers and the heights of their sons. Refer to theStatCrunch display and answer the given questions or identify the indicated items.

The display is based on Data Set 5 “Family Heights” in Appendix B.

Identify the multiple regression equation that expresses the height of a son in terms of the height of his father and mother.
See all solutions

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