Ms. Gilford's Math - Home



Name: ________________________Correlation PracticeIn each of the following relationships, is r > 0 or r < 0? Closer to r = 0 or r = ± 1? Explain your reasoning.1. 2. 3. 4. 4368800182880005. Points and turnovers There is a linear relationship between the number of turnovers and the number of points scored for players in the 2013–2014 NBA season. The correlation for these data is r = 0.92. Interpret this value. 436880012010006. It’s warmer down here There is a roughly linear relationship between the latitude of major American cities and the average temperature in July. The correlation for the 12 cities with the largest populations is r 5 20.55.24 Interpret this value. 7. GPA linked to pencils? For their final statistics project, Jordynn and Angie surveyed a random sample of 50 students at their school. Each student in the survey reported his or her GPA and the number of pencils in his or her possession at the moment. The association between number of pencils and GPA is linear, with a correlation of r = -0.23. Does the negative association suggest that carrying fewer pencils will increase a student’s GPA? Explain. 8. Long courtship, long marriage? A psychologist who specializes in divorce counseling finds that among his patients there is a linear relationship between the number of years of courtship before marriage and the number of years the couple stays married. The correlation is r = 0.76. Does this suggest that waiting a few years before getting married will make your marriage last longer? Explain. 9. More points, more turnovers? Refer to Question 5. Does the fact that r = 0.92 suggest that an increase in turnovers will cause NBA players to score more points? Explain. 10. Crying for higher IQ? Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants 4 to 10 days old and their IQ test scores at age 3. A snap of a rubber band on the sole of the foot caused the infants to cry. The researchers recorded the crying and measured its intensity by the number of peaks in the most active 20 seconds. Does the fact that r = 0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain. 43685801780811. Tipping at a buffet Do customers who stay longer at buffets give larger tips? Charlotte, a statistics student who worked at an Asian buffet, decided to investigate this question for her second-semester project. While working as a hostess, she obtained a random sample of receipts, which included the length of time (in minutes) the party was in the restaurant and the amount of the tip (in dollars). Here is a scatterplot of these data.(a) Interpret the value r = 0.36. (b) Does increasing the amount of time spent in the restaurant cause an increase in the amount of the tip? Explain.12. Match the correlations Suppose that a PE teacher collected data about the students in her class. Some of these variables included number of pull-ups in 1?minute, number of push-ups in 1 minute, number of sit-ups in 1 minute, and weight. The teacher then calculated the correlation for the following relationships: ? Number of pull-ups and number of push-ups ? Number of pull-ups and number of sit-ups ? Number of pull-ups and weight The correlations for these relationships are r = 0.9, r = -0.5, r = 0.3. Which correlation goes with which relationship? Explain.13. Husbands and wives Suppose that women always married men who were 2 years older than they are. What is the correlation between the ages of wives and husbands? Explain your reasoning. ................
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