The abstract of a study (Postma, 2014, “A relationship between attractiveness and performance in professional cyclists.” Biol. Lett., doi: 10:20130966) reads: “Females often prefer to mate with high quality males, and one aspect of quality is physical performance. Although a preference for physically fitter males is therefore predicted, the relationship between attractiveness and performance has rarely been quantified.

Here, I [...] ask whether variation in (endurance) performance is associated with variation in facial attractiveness within elite professional cyclists that finished the 2012 Tour de France[...].” The data from this study are available on the book’s website and contain a column called

“Performance” that is a composite score of the time it took each rider to complete the Tour de France prologue, the two individual timed trials, and the complete race. Smaller values indicate faster, i.e., better, performing riders. The data also contains a variable called “Attractiveness.” To obtain this attractiveness score, the portrait of each rider was rated by several persons on a scale from 1 to 5, and the average rating is reported in this column.

a. In the context of this study, which variable plays the role of the (i) explanatory variable, (ii) response variable?

b. Construct an appropriate plot to analyze the relationship between performance and attractiveness. (The Scatterplots & Correlation app has this data set preloaded under the name “Tour de France”.)

c. Based on the scatterplot, do you expect the correlation coefficient r to be positive or negative? Why?

d. Find the correlation coefficient r and write a short paragraph describing the relationship. (Comment on whether the relationship is approximately linear and its direction and strength.)

e. Do you think performance is a good predictor for attractiveness for these riders?