soln%203 - X X X X X X X X X X X X X X X X X AP Statistics...

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X X X X X X X X X X X X X X X X X AP Statistics Solutions to Packet 3 X Examining Relationships Scatterplots Correlation Least-Squares Regression X X X X X X X X X X X X X
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2 HW #15 1, 3, 6, 7, 9, 10 3.1 EXPLANATORY AND RESPONSE VARIABLES In each of the following situations, is it more reasonable to simply explore the relationship between the two variables or to view one of the variables as an explanatory variable and the other as a response variable? Is the latter case, which is the explanatory variable and which is the response variable? (a) The amount of time a student spends studying for a statistics exam and the grade of the exam. Time spent studying is explanatory; the grade is the response variable. (b) The weight and height of a person. Explore the relationship; there is no reason to view one or the other as explanatory. (c) The amount of yearly rainfall and the yield of a crop. Rainfall is explanatory; crop yield is the response variable. (d) A student’s grade in statistics and in French. Explore the relationship. (e) The occupational class of a father and of a son. The father’s class is explanatory; the son’s class is the response variable. 3.3 GENDER GAP There may be a “gender gap” in political party preference in the United States, with women more likely than men to prefer Democratic candidates. A political scientist selects a large sample of registered voters, both men and women. She asks each voter whether they voted for the Democratic or Republican candidate in the last congressional election. What are the explanatory and response variables in this study? Are they categorical or quantitative? Gender is explanatory, and political preference in the last election is the response. Both are categorical.
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3 3.6 THE ENDANGERED MANATEE Manatees are large, gentle sea creatures that live along the Florida coast. Many manatees are killed or injured by powerboats. Here are data on powerboat registrations (in thousands) and the number of manatees killed by boats in Florida in the years 1977 to 1990: Year Powerboat registrations (1000) Manatees killed Year Powerboat registrations (1000) Manatees killed 1977 1978 1979 1980 1981 1982 1983 447 460 481 498 513 512 526 13 21 24 16 24 20 15 1984 1985 1986 1987 1988 1989 1990 559 585 614 645 675 711 719 34 33 33 39 43 50 47 (a) We want to examine the relationship between number of powerboats and number of manatees killed by boats. Which is the explanatory variable? Explanatory variable = number of powerboat registrations. (b) Make a scatterplot of these data. ( Be sure to label the axes with the variable names, not just x and y.) What does the scatterplot show about the relationship between these variables? The plot shows a moderately strong positive linear relationship. As registrations increase, the number of manatee deaths also tends to increase.
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4 3.7 ARE JET SKIS DANGEROUS? Propelled by a stream of pressurized water, jet skis and other so-called wet bikes carry from one to three people, retail for an average price of $5,700, and have become one of the most popular types of recreational vehicle sold today. But critics say they are noisy, dangerous, and damaging to the environment.
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This note was uploaded on 03/01/2010 for the course STAT AP taught by Professor Kalliongis during the Spring '10 term at Kirkwood.

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soln%203 - X X X X X X X X X X X X X X X X X AP Statistics...

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