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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 鈥渨eight of bears鈥� is explained by the linear relationship between the variables 鈥渨eight,鈥� 鈥渓ength,鈥� and 鈥渃hest size鈥�.

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 鈥渨eight,鈥� 鈥渓ength,鈥� and 鈥渃hest size.鈥�

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 鈥渨eight of bears鈥� as the response variable and 鈥渓ength鈥� and 鈥渃hest size.鈥�

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.

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Most popular questions from this chapter

Cell Phones and Driving In the author鈥檚 home town of Madison, CT, there were 2733 police traffic stops in a recent year, and 7% of them were attributable to improper use of cell phones. Use a 0.05 significance level to test the claim that the sample is from a population in which fewer than 10% of police traffic stops are attributable to improper cell phone use.

What is the difference between the regression equation\(\hat y = {b_0} + {b_1}x\)and the regression equation\(y = {\beta _0} + {\beta _1}x\)?

Testing for a Linear Correlation. In Exercises 13鈥�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.)

Oscars Listed below are ages of Oscar winners matched by the years in which the awards were won (from Data Set 14 鈥淥scar Winner Age鈥� in Appendix B). Is there sufficient evidence to conclude that there is a linear correlation between the ages of Best Actresses and Best Actors? Should we expect that there would be a correlation?

Actress

28

30

29

61

32

33

45

29

62

22

44

54

Actor

43

37

38

45

50

48

60

50

39

55

44

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Stocks and Sunspots. Listed below are annual high values of the Dow Jones Industrial Average (DJIA) and annual mean sunspot numbers for eight recent years. Use the data for Exercises 1鈥�5. A sunspot number is a measure of sunspots or groups of sunspots on the surface of the sun. The DJIA is a commonly used index that is a weighted mean calculated from different stock values.

DJIA

14,198

13,338

10,606

11,625

12,929

13,589

16,577

18,054

Sunspot

Number

7.5

2.9

3.1

16.5

55.7

57.6

64.7

79.3

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\({s_e}\)Notation Using Data Set 1 鈥淏ody Data鈥� 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.
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