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# Chapter 10, Section 2,3,4 Problem 16, Problem 26

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For Problems 16 and 26, construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table A-6 using x = 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 10-3 exercises.)

Chapter 10, Section 2
Problem 16

Heights of Presidents and Runners-Up. Theories have been developed about the heights of winning candidates for the U.S. presidency and the heights of candidates who were runner-up. Listed below are heights (in inches) from recent presidential elections. Is there a linear correlation between the heights of candidates who won and the heights of the candidates who were runners-up?

Winner 69.5 73 73 74 74.5 74.5 71 71
Runner-Up 72 69.5 70 68 74 74 73 76

Problem 26

Crickets and Temperature. One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 min and the corresponding temperatures in Fahrenheit (based on data from The Song of Insects by George W. Pierce, Harvard University Press). Is there a linear correlation between the number of chirps in 1 min and the temperature?

Chirps in 1 min 882 1188 1104 864 1200 1032 960 900
Temperature (F) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6

For Problems 16 and 26, Finding the Equation of the Regression Line and Making Predictions. (Use the same data set from above. 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.

Chapter 10, Section 3
Problem 16

Heights of Presidents and Runners-Up. Find the best predicted height of runner-up Goldwater, given that the height of the winning presidential candidate Johnson is 75 in. Is the predicted height of Goldwater close to his actual height of 72 in.?
Winner 69.5 73 73 74 74.5 74.5 71 71
Runner-Up 72 69.5 70 68 74 74 73 76

Problem 26

Crickets and Temperature. Find the best predicted temperature (in Fahrenheit) at a time when a cricket chirps 3000 times in one minute. What is wrong with this predicted value?
Chirps in 1 min 882 1188 1104 864 1200 1032 960 900
Temperature (F) 69.7 93.3 84.3 76.3 88.6 82.6 71.6 79.6

Finding Measures of Variation. Find the (a) explained variation, (b) unexplained variation, (c) total variation, (d) coefficient of determination, and (e) standard error of estimate s. In each case, there is sufficient evidence to support a claim of a linear correlation so that it is reasonable to use the regression equation when making predictions. (Results from these exercises are used in Exercises 17 - 20).

Chapter 10, Section 4
Problem 16

Global Warming. Listed below are concentration (in parts per million) of CO2 and temperatures (in Celsius) for different years (based on data from the Earth Policy Institute).
CO2 314 317 320 326 331 339 346 354 361 369
Temperature13.9 14.0 13.9 14.1 14.0 14.3 14.1 14.5 14.5 14.4