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Chapter 3 3.1 (a) The amount of time a student spends studying is the explanatory variable and the grade on the exam is the response variable. (b) Height is the explanatory variable and weight is the response variable. (c) Inches of rain is the explanatory variable and the yield of corn is the response variable. (d) It is more reasonable to explore the relationship between a student’s grades in statistics and French. (e) A family’s income is the explanatory variable and the years of education their eldest child completes is the response variable. 3.2 The explanatory variable is weight of a person, and the response variable is mortality rate (that is, how likely a person is to die over a 10-year period). The other variables that may influence the relationship between weight and survival are the amount of physical activity, perhaps measured by hours of exercise per week, and economic status, which could be measured by annual income of the person, family net worth, amount of savings, or some other financial variable. 3.3 Water temperature is the explanatory variable, and weight change (growth) is the response variable. Both are quantitative. 3.4 The explanatory variable is the type of treatment—removal of the breast or removal of only the tumor and nearby lymph nodes, followed by radiation, and survival time is the response variable. Type of treatment is a categorical variable, and survival time is a quantitative variable. 3.5 (a) The explanatory variable is the number of powerboat registrations. (b) A scatterplot is shown below. Powerboat Registrations (1000s)Manatees killed7507006506005505004505040302010The scatterplot shows a positive linear relationship between these variables. (c) There is a positive linear association between powerboat registrations and manatees killed. (d) Yes, the relationship between these variables is linear. (e) The relationship is a strong, positive, linear association. Yes, the number of manatees killed can be predicted accurately from powerboat registrations. For 719,000 powerboat registrations, about 48 manatees would be killed by powerboats. 3.6 (a) A scatterplot is shown below. 56Chapter 3