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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

The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

The sample data result in a linear correlation coefficient of r= 0.499 and the regression equation\(\hat y = 3.83 + 2.39x\). What is the best predicted number of burglaries, given an enrollment of 50 (thousand), and how was it found?

The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

Repeat the preceding exercise, assuming that the linear correlation coefficient is r= 0.997.

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










Two Independent Samples The methods of Section 9-2 can be used to test the claim that two populations have the same mean. Identify the specific claim that the treatment is effective, then use the methods of Section 9-2 to test that claim. The methods of Section 9-2 are based on the requirement that the samples are independent. Are they independent in this case?

Explore! Exercises 9 and 10 provide two data sets from “Graphs in Statistical Analysis,” by F. J. Anscombe, the American Statistician, Vol. 27. For each exercise,

a. Construct a scatterplot.

b. Find the value of the linear correlation coefficient r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot.

x

10

8

13

9

11

14

6

4

12

7

5

y

9.14

8.14

8.74

8.77

9.26

8.10

6.13

3.10

9.13

7.26

4.74

In Exercises 9–12, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 20 “Car Measurements” in Appendix B. The response (y) variable is CITY (fuel consumption in mi, gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi, gal).

A Honda Civic weighs 2740 lb, it has an engine displacement of 1.8 L, and its highway fuel consumption is 36 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate?
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