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Olympic figure skating For many people, the womens figure skating competition is the
Chapter 3, Problem 55(choose chapter or problem)
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. 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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Questions & Answers
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. 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 \(r^2\)
ANSWER:Step 1 of 6
Given,
Number of skaters, \(n=24\)
The standard deviation of the residuals, \(s=10.2\)
The coefficient of determination, \(r^{2}=0.736\)
The equation of the least-squares regression line for predicting scores in the free skate from the scores in the short program,
\(\hat{y}=-16.2+2.07 x\)
Using the scatterplot and residual plot we have to determine the following: