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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

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?

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.)

Sports Repeat the preceding exercise using diameters and volumes.

Finding Critical r Values Table A-6 lists critical values of r for selected values of n and a. More generally, critical r values can be found by using the formula

\(r = \frac{t}{{\sqrt {{t^2} + n - 2} }}\)

where the t value is found from the table of critical t values (Table A-3) assuming a two-tailed case with n - 2 degrees of freedom. Use the formula for r given here and in Table A-3 (with n - 2 degrees of freedom) to find the critical r values corresponding to \({H_1}:\rho \ne 0\), \(\alpha \)= 0.02, and n = 27.

Interpreting the Coefficient of Determination. In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Crickets and Temperature r = 0.874 (x = number of cricket chirps in 1 minute, y = temperature in °F)

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.)

Pizza and the Subway The “pizza connection” is the principle that the price of a slice of pizza in New York City is always about the same as the subway fare. Use the data listed below to determine whether there is a significant linear correlation between the cost of a slice of pizza and the subway fare.

Year

1960

1973

1986

1995

2002

2003

2009

2013

2015

Pizza Cost

0.15

0.35

1

1.25

1.75

2

2.25

2.3

2.75

Subway Fare

0.15

0.35

1

1.35

1.5

2

2.25

2.5

2.75

CPI

30.2

48.3

112.3

162.2

191.9

197.8

214.5

233

237.2

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