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Chapter 10: Q1BSC (page 468)

\({s_e}\)Notation Using Data Set 1 “Body Data” in Appendix B, if we let the predictor variable x represent heights of males and let the response variable y represent weights of males, the sample of 153 heights and weights results in\({s_e}\)= 16.27555 cm. In your own words, describe what that value of \({s_e}\)represents.

Short Answer

Expert verified

The value of \({s_e}\) equal to 16.27555 cm explains that the average distance of the observed value of weights of males from the fitted values is obtained using the regression equation.

Step by step solution

01

Given information

A regression equation between the response variable “weights of male” and the predictor variable “heights of males” is given.

The value of \({s_e}\) is 16.27555 cm.

02

Meaning of \({s_e}\)

\({s_e}\)stands for the standard error of the estimate.

It describes the mean distance between the observed values of the response variable and the predicted values.

Here, the response variable is the weights of males, and the standard error of the estimate\(\left( {{s_e}} \right)\)is 16.27555 cm.

Thus, the standard error of estimate tells that the average difference between the measured weights and the weights predicted by the regression equation equals 16.27555 cm.

It represents how much the sample points deviate from the regression line.

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Most popular questions from this chapter

Coefficient of Determination Using the heights and weights described in Exercise 1, the linear correlation coefficient r is 0.394. Find the value of the coefficient of determination. What practical information does the coefficient of determination provide?

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).

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DJIA

14,198

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10,606

11,625

12,929

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Sunspot Number

7.5

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55.7

57.6

64.7

79.3

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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 (fontanels) (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 Duragestic 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 Duragestic Treatment

0.4

1.4

1.8

2.9

6.0

1.4

0.7

3.9

0.9

1.8

0.9

9.3

8.0

6.8

2.3

0.4

0.7

1.2

4.5

2.0

1.6

2.0

2.0

6.8

6.6

4.1

4.6

2.9

5.4

4.8

4.1

Regression:Use the given data to find the equation of the regression line. Let the response (y) variable be the pain intensity after treatment. What would be the equation of the regression line for a treatment having absolutely no effect?

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