Chapter 10: Q2BSC (page 468)
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?
No, 0 correlation does not indicate that there is no association between the two variables.
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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).
If exactly two predictor (x) variables are to be used to predict the city fuel consumption, which two variables should be chosen? Why?
Adjusted Coefficient of Determination For Exercise 2, why is it better to use values of adjusted \({R^2}\)instead of simply using values of \({R^2}\)?
Interpreting r. In Exercises 5–8, use a significance level of A = 0.05 and refer to the accompanying displays.
5. Bear Weight and Chest Size Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in Data Set 9 “Bear Measurements” in Appendix B; results are shown in the accompanying Statdisk display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight?
Global Warming If we find that there is a linear correlation between the concentration of carbon dioxide (\(C{O_2}\)) in our atmosphere and the global mean temperature, does that indicate that changes in (\(C{O_2}\))cause changes in the global mean temperature? Why or why not?
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.)
Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population (based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1). Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities?
Lemon Imports | 230 | 265 | 358 | 480 | 530 |
Crash Fatality Rate | 15.9 | 15.7 | 15.4 | 15.3 | 14.9 |
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