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# Olympic figure skating For many people, the womens figure skating competition is the

**Chapter 3, Problem 55**

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**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 \(r^2\)

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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: