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Chapter 10: Q8CQQ (page 468)

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).

Enrollment (thousands)

53

28

27

36

42

Burglaries

86

57

32

131

157

True or false: If there is no linear correlation between enrollment and number of burglaries, then those two variables are not related in any way.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Given information

A table represents the number of enrolled students (in thousands) and the burglaries for randomly selected large colleges

02

Describe the correlation

Linear correlation is a measure that finds the magnitude of linear association between two variables. The measure for Pearson’s correlation is between –1 and 1 where 1 and -1 respectively indicates perfect positive and negative linear relationships.

The two variables can be associated by any pattern—linear or non-linear.

Thus, the given statement is false as the variables can be non-linearly related if there is no linear correlation between enrollment and number of burglaries.

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Most popular questions from this chapter

In Exercises 5–8, use a significance level 0.05 and refer to theaccompanying displays.Cereal Killers The amounts of sugar (grams of sugar per gram of cereal) and calories (per gram of cereal) were recorded for a sample of 16 different cereals. TI-83>84 Plus calculator results are shown here. Is there sufficient evidence to support the claim that there is a linear correlation between sugar and calories in a gram of cereal? Explain.

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female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings are from Data Set 18 “Speed Dating” in Appendix B. The 50 paired ratings yield\(\bar x = 6.5\),\(\bar y = 5.9\), r= -0.277, P-value = 0.051, and\(\hat y = 8.18 - 0.345x\). Find the best predicted value of\(\hat y\)(attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 8.

Confidence Intervals for a Regression Coefficients A confidence interval for the regression coefficient b1 is expressed

\(\begin{array}{l}{b_1} - E < {\beta _1} < {b_1} + E\\\end{array}\)

Where

\(E = {t_{\frac{\alpha }{2}}}{s_{{b_1}}}\)

The critical t score is found using n –(k+1) degrees of freedom, where k, n, and sb1 are described in Exercise 17. Using the sample data from Example 1, n = 153 and k = 2, so df = 150 and the critical t scores are \( \pm \)1.976 for a 95% confidence level. Use the sample data for Example 1, the Stat diskdisplay in Example 1 on page 513, and the Stat Crunchdisplay in Exercise 17 to construct 95% confidence interval estimates of \({\beta _1}\) (the coefficient for the variable representing height) and\({\beta _2}\) (the coefficient for the variable representing waist circumference). Does either confidence interval include 0, suggesting that the variable be eliminated from the regression equation?

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).

Which regression equation is best for predicting city fuel consumption? Why?

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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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