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Terminology Using the lengths (in.), chest sizes (in.), and weights (lb) of bears from Data Set 9 “Bear Measurements” in Appendix B, we get this regression equation: Weight = -274 + 0.426 Length +12.1 Chest Size. Identify the response and predictor variables

Short Answer

Expert verified

The response variable is the weight of bears (in lb), and the predictor variables are the length (in inches) and chest size (in inches).

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

Response variable

In a regression equation, the variable predicted in the equation depends on other independent variables. It is called the response variable.

Here, the weight of the bear needs to be predicted from the equation, and it depends on two other variables.

Thus, the variable weight is the response variable.

03

Predictor variables

An independent variable utilized in an equation to predict another variable is called the predictor variable.

In the given equation, length and chest size are used to predict weight.

Thus, length and chest size are predictor variables.

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Most popular questions from this chapter

Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Use the CPI/subway fare data from the preceding exercise and find

the best predicted subway fare for a time when the CPI reaches 500. What is wrong with this prediction?

Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493.

Internet and Nobel Laureates Find the best predicted Nobel Laureate rate for Japan, which has 79.1 Internet users per 100 people. How does it compare to Japan’s Nobel Laureate rate of 1.5 per 10 million people?

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?

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?

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

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