Homework_2_Solutions

Homework_2_Solutions - drink more beer The observed...

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Homework 2 Solutions 5.2 a. Negative association. As percentage taking the test increases, average math SAT decreases. b. More or less linear. There could be a slight curvature but a straight line appears to be a suitable description of the pattern. c. Highest math Sat was around 600; about 5%, perhaps fewer, took the test in that state. d. Lowest math SAT was around 475; about 60% took the test in that state. 5.21 1.7 and 2.5. They are not between 1 and +1. 5.25 A correlation of 0.6 implies a stronger linear relationship than a correlation of +0.4 because in absolute magnitude it is closer to 1. To judge the strength of a linear relationship, ignore the sign of a correlation coefficient. 5.29 a. Graph 2 shows the strongest relationship while Graph 3 shows the weakest. b. Graph 1: +0.6; Graph 2: 0.9; Graph 3: 0; Graph 4: +0.3. 5.50 No, this does not mean that increasing a person’s income will cause him or her to
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Unformatted text preview: drink more beer. The observed relationship probably results from how economic inflation and population growth influence both variables through the years. Note also that we only have aggregate data for the whole country, which is not data directly relevant to individual behavior. 5.69 a. The correlation between winning time and year is negative because the slope ( − .1094) is negative. b. y ˆ =255 − (.1094)(1994) = 36.86 seconds. The actual 1994 winning time of 36.33 seconds is 0.53 seconds faster than the prediction. c. Winning times decrease, on average, by .1094 seconds per year. d. The data used for the regression equation was for the years 1924 to 1992. Extrapolating as far beyond this range of years as 2050 could be extremely misleading. It is expected that the winning times will taper off eventually. The human body has limits and the winning times cannot keep decreasing at the same rate forever....
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