Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Q4BSC (page 468)

Interpreting\({R^2}\)For the multiple regression equation given in Exercise 1, we get \({R^2}\)= 0.928. What does that value tell us?

Short Answer

Expert verified

The value \({R^2} = 0.928\) indicates that 92.8% variation in the response variable “weight of bears” is explained by the linear relationship between the variables “weight,” “length,” and “chest size”.

Step by step solution

01

Given information

A regression equation is computed to predict the weight of a bear (in lb) using the linear relationship between the variables “weight,” “length,” and “chest size.”

02

Interpretation of \({R^2}\)

The value of \({R^2}\) for a regression model implies how good the predicted model is.

In other words, it indicates the percentage of variation explained by the linear relation of the response variables with the predictor variables.

Here, a regression equation is constructed with “weight of bears” as the response variable and “length” and “chest size.”

The value of\({R^2} = 0.928\)indicates that 92.8% variation in the weight of bears can be explained by their lengths and chest sizes.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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.

A son will be born to a father who is 70 in. tall and a mother who is 60 in. tall. Use the multiple regression equation to predict the height of the son. Is the result likely to be a good predicted value? Why or why not?

Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

Internet and Nobel Laureates Listed below are numbers of Internet users per 100 people and numbers of Nobel Laureates per 10 million people (from Data Set 16 “Nobel Laureates and Chocolate” in Appendix B) for different countries. Is there sufficient evidence to conclude that there is a linear correlation between Internet users and Nobel Laureates?

Internet Users

Nobel Laureates

79.5

5.5

79.6

9

56.8

3.3

67.6

1.7

77.9

10.8

38.3

0.1

Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population (based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1). Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities?

Lemon Imports

230

265

358

480

530

Crash Fatality Rate

15.9

15.7

15.4

15.3

14.9

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?

Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of A = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables. (Save your work because the same data sets will be used in Section 10-2 exercises.)

Old Faithful Listed below are duration times (seconds) and time intervals (min) to the next eruption for randomly selected eruptions of the Old Faithful geyser in Yellowstone National Park. Is there sufficient evidence to conclude that there is a linear correlation between duration times and interval after times?

Duration

242

255

227

251

262

207

140

Interval After

91

81

91

92

102

94

91
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free