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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 sk...

Question

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 $\hat{y}=-16.2+2.07 x .$ Also, $s=10.2$ and $

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 $\hat{y}=-16.2+2.07 x .$ Also, $s=10.2$ and $r^{2}=0.736$ (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 $r^{2}$.



Answers

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 $\hat{y}=-16.2+2.07 x .$ Also, $s=10.2$ and $r^{2}=0.736$ (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 $r^{2}$.


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