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Chapter 10: Q4BSC (page 468)
Scatterplots Match these values of r with the five scatterplots shown below: 0.268, 0.992, -1, 0.746, and 1.
The r values for the five scatterplots are:
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Exercises 13鈥�28 use the same data sets as Exercises 13鈥�28 in Section 10-1. 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 on page 493.
Use the shoe print lengths and heights to find the best predicted height of a male who has a shoe print length of 31.3 cm. Would the result be helpful to police crime scene investigators in trying to describe the male?
Exercises 13鈥�28 use the same data sets as Exercises 13鈥�28
in Section 10-1. 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 on page 493.
Find the best predicted temperature at a time when a cricket
chirps 3000 times in 1 minute. What is wrong with this predicted temperature?
Notation Twenty different statistics students are randomly selected. For each of them, their body temperature (掳C) is measured and their head circumference (cm) is measured.
a. For this sample of paired data, what does r represent, and what does \(\rho \)represent?
b. Without doing any research or calculations, estimate the value of r.
c. Does r change if the body temperatures are converted to Fahrenheit degrees
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 鈥�(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?
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.)
Internet and Nobel Laureates Listed below are numbers of Internet users per 100 people and numbers of Nobel Laureates per 10 million people (from Data Set 16 鈥淣obel Laureates and Chocolate鈥� in Appendix B) for different countries. Is there sufficient evidence to conclude that there is a linear correlation between Internet users and Nobel Laureates?
Internet Users | Nobel Laureates |
79.5 | 5.5 |
79.6 | 9 |
56.8 | 3.3 |
67.6 | 1.7 |
77.9 | 10.8 |
38.3 | 0.1 |
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