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Unformatted text preview: STAT 200 Chapter 2 Looking at Data - Relationships The following are the advertised horsepower ratings and expected gas mileage for 14 vehicles. Vehicle Horsepower (hp) Gas mileage (mpg) Origin of the car 1 170 22 European 2 205 20 American 3 190 15 American 4 125 31 American 5 310 10 American 6 285 13 American 7 127 29 Asian 8 140 25 Asian 9 215 21 Asian 10 210 23 American 11 170 18 Asian 12 140 23 American 13 194 21 Asian 14 115 29 European What type of variables are the horsepower and gas mileage variables? Question of interest: Do vehicles with higher horsepower tend to be less fuel efficient? In this chapter, we will be examining the relationship between two quantitative variables. Scatterplots (Section 2.1) help visualize possible relationship between two quantitative (but not categorical) vari- ables a plot of pairs of observations on the x- y plane, e.g., x i = horsepower of vehicle i , y i = gas mileage of vehicle i the mean-mean point ( x, y ) provides the center of the cloud of data points: e.g., x = 185 . 4 hp , y = 21 . 4 mpg 1 Here is the scatterplot of the horsepower and gas mileage for the 14 vehicles. The horsepower readings are plotted on the horizontal ( x ) axis, and the gas mileage data are plotted on the vertical ( y ) axis. Each vehicle is represented by a point in the plot. Roles for variables Which of the two variables to plot on the x-axis and which on the y-axis? explanatory variable to be plotted on the x-axis response variable to be plotted on the y-axis The explanatory variable is believed to have some influence on the value of the response variable. However, it is not always apparent which is the explanatory variable and which is the re- sponse variable, e.g., relationship between height and weight of toddlers. In such a case, either variable can go on the x-axis....
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- Spring '08