Two Quantitative Variables 75 70 60 55 25 30 Foot length (cm) 35 acters and +E" in + E' in Mac. FIGURE 10.3.5 Heights and foot lengths color coded by blue= male and orange = female. 17. How do the female foot lengths tend to compare to the male foot lengths? How do the female heights tend to compare to the male height? Smaller and shorter. 18. What do you notice about the slopes and intercepts for the two lines? How do you interpret these differences in this context? racters and 1+E" in +E" in Mac. The least squares regression line for men is predicted height = 44.03 + 0.8561(foot length), and the least squares regression line for women is predicted height=45.90+0.7152(foot length). 19. What do you think the R will be just for the men? Just for the women? How do you think these values will compare to the overall R of 0.506? Why? racters and -1+E" in +E" in Mac. In this case, the R for the female-only data is 0.116 and for the male-only data is 0.267. Both groups have lower R values than the overall R. R measures how close the observations are to their respective lines. When we examine only the female data, the residuals are large relative to the smaller variation in female heights. Whereas the combined line (ignoring sex) has similar residuals, they are smaller compared to the larger total variation in heights.