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Examining Relationships • So far we have primarily focused on a single variable. • It is often more interesting to examine the relationship between variables. • For now, we will focus on relationships between two quantitative variables. 1 Roles for Variables • Response Variable – Often the variable we are most interested in • Explanatory Variable (Predictor) – Used to explain the variation in the response variable 2 Scatterplots • Scatterplots are a common and effective way to visualize the relationship between two quantitative variables • When describing the association, or relationship, between two variables, always look at the overall pattern and deviations from the pattern. 3 1 Teenage Drug Use • Is there a relationship between the use of marijuana and the use of other drugs? • A survey was conducted in the U.S. and in 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. • A scatterplot of the data follows. 4 Teenage Drug Use Bivariate Fit of Other Drugs (%) By Marijuana (%) Other Drugs (%) 40 30 20 10 0 0 10 20 30 40 50 60 Marijuana (%) 5 Positive Association • Above average values of marijuana usage are associated with above average values of the usage of other illegal drugs. • Below average values of marijuana usage are associated with below average values of the usage of other illegal drugs. 6 2 Price of Used Cars • Is there a relationship between the age of a car and its price? • A scatterplot of the ages and prices of 17 used Toyota Corollas follows. 7 Price of Used Cars Bivariate Fit of Prices Advertised ($) By Age (yr) 15000 Prices Advertised ($) 12500 10000 7500 5000 2500 0 0 2.5 5 7.5 10 12.5 15 Age (yr) 8 Negative Association • Above average values of car age are associated with below average values of car price. • Below average values of car age are associated with above average values of car price. 9 3