Olympic figure skating For many people, the women’s figure skating competition is the highlight of the Olympic Winter Games. Scores in the short program x and scores in the free skate y were recorded for each of the 24 skaters who competed in both rounds during the 2010 Winter Olympics in Vancouver, Canada.21 A regression analysis was performed using these data.

The scatterplot and residual plot follow. The equation of the least-squares regression line is y^ = −16.2 + 2.07x. Also, s = 10.2 and r2 = 0.736.

(a) Calculate and interpret the residual for the gold medal winner, Yu-Na Kim, who scored 78.50 in the short program and 150.06 in the free skate.

(b) Is a linear model appropriate for these data? Explain.

(c) Interpret the value of s.

(d) Interpret the value of r2.

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Free skate score Residual 160 140 20 120 100 80 20 20 10 0 -10 -201 45 50 55 60 65 70 75 80 Short program score -30 45 50 55 60 65 70 75 80 Short program score