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Chapter 10: Q10BSC (page 468)

In Exercises 9鈥�12, refer to the accompanying table, which was obtained using the data from 21 cars listed in Data Set 20 鈥淐ar Measurements鈥� 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).

If exactly two predictor (x) variables are to be used to predict the city fuel consumption, which two variables should be chosen? Why?

Short Answer

Expert verified

The model with predictors HWY and WT are the best to predict the city fuel consumption.

Step by step solution

01

Given information

The table representing the predictor variables, P-value, \({R^2}\) , Adjusted \({R^2}\)and the regression equations are provided.

02

Discuss the measures stated in the table

The three measures stated in the table are:

  • P-value: to decide the significance of the model
  • \({R^2}:\)to indicate the accuracy of the model and the fitness of the regression model
  • Adjusted \({R^2}:\)to measure the accuracy of the model by evaluating the counts of independent variables
03

Identify the best model

From the table, the two variable model that has the smallest P-value (0.0000), t highest\({R^2}\)and adjusted\({R^2}\)values (0.942 and 0.935 respectively) correspond to the WT/HWY predictor variable.

This implies that the HWY and WT predictor models are the best to predict the city鈥檚 fuel consumption.

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The following exercises are based on the following sample data consisting of numbers of enrolled students (in thousands) and numbers of burglaries for randomly selected large colleges in a recent year (based on data from the New York Times).

The sample data result in a linear correlation coefficient of r= 0.499 and the regression equation\(\hat y = 3.83 + 2.39x\). What is the best predicted number of burglaries, given an enrollment of 50 (thousand), and how was it found?

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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.)

Manatees Listed below are numbers of registered pleasure boats in Florida (tens of thousands) and the numbers of manatee fatalities from encounters with boats in Florida for each of several recent years. The values are from Data Set 10 鈥淢anatee Deaths鈥� in Appendix B. Is there sufficient evidence to conclude that there is a linear correlation between numbers of registered pleasure boats and numbers of manatee boat fatalities?

Pleasure Boats

99

99

97

95

90

90

87

90

90

Manatee Fatalities

92

73

90

97

83

88

81

73

68

Cigarette Nicotine and Carbon Monoxide Refer to the table of data given in Exercise 1 and use the amounts of nicotine and carbon monoxide (CO).

a. Construct a scatterplot using nicotine for the xscale, or horizontal axis. What does the scatterplot suggest about a linear correlation between amounts of nicotine and carbon monoxide?

b. Find the value of the linear correlation coefficient and determine whether there is sufficient evidence to support a claim of a linear correlation between amounts of nicotine and carbon monoxide.

c. Letting yrepresent the amount of carbon monoxide and letting xrepresent the amount of nicotine, find the regression equation.

d. The Raleigh brand king size cigarette is not included in the table, and it has 1.3 mg of nicotine. What is the best predicted amount of carbon monoxide?

Tar

25

27

20

24

20

20

21

24

CO

18

16

16

16

16

16

14

17

Nicotine

1.5

1.7

1.1

1.6

1.1

1.0

1.2

1.4

Interpreting r For the same two variables described in Exercise 1, if we find that r = 0, does that indicate that there is no association between those two variables?
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