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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 skate ?y were recorded for each of the 24 skaters who competed in both rounds during the 2010 Winter Olympics in Vancouver, Canada. Here is a scatterplot with least-squares regression line ?=–16.2+2.07?y=–16.2+2.07⁢x. For this model, ?=10.2s=10.2 and ?2=0.736r2=0.736.

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. Here is a scatterplot with least-squares regression line ?=–16.2+2.07?y=–16.2+2.07⁢x. For this model, ?=10.2s=10.2 and ?2=0.736r2=0.736.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 skate ?y were recorded for each of the 24 skaters who competed in both rounds during the 2010 Winter Olympics in Vancouver, Canada. Here is a scatterplot with least-squares regression line ?=–16.2+2.07?y=–16.2+2.07⁢x. For this model, ?=10.2s=10.2 and ?2=0.736r2=0.736.

The image displays a scatterplot with a least-squares regression line for figure skating scores. The x-axis represents the "Short program score," ranging from 40 to 80, while the y-axis represents the "Free skate score," ranging from 60 to 160. Data points are scattered around the positive-sloping regression line, indicating a correlation between the two scores. Key details about the model are: - The equation of the regression line is \( y = 10.2 + 2.07x \). - The standard deviation of the residuals, \( s \), is 10.2. - The coefficient of determination, \( R^2 \), is 0.736. Interpretation options for the \( R^2 \) value are provided: - For each one-point increase in the short program score, the model predicts about a 73.6% increase in the free skate score. - About 73.6% of the free skate score is accounted for by the least-squares regression line with \( x = \) short program score. - About 73.6% of the variability in the free skate score is accounted for by the least-squares regression line with \( x = \) short program score. - There is a strong, positive, linear association between the free skate score and short program score. - About 73.6% of the variability in the short program score is accounted for by the least-squares regression line with \( x = \) free skate score.
Transcribed Image Text:The image displays a scatterplot with a least-squares regression line for figure skating scores. The x-axis represents the "Short program score," ranging from 40 to 80, while the y-axis represents the "Free skate score," ranging from 60 to 160. Data points are scattered around the positive-sloping regression line, indicating a correlation between the two scores. Key details about the model are: - The equation of the regression line is \( y = 10.2 + 2.07x \). - The standard deviation of the residuals, \( s \), is 10.2. - The coefficient of determination, \( R^2 \), is 0.736. Interpretation options for the \( R^2 \) value are provided: - For each one-point increase in the short program score, the model predicts about a 73.6% increase in the free skate score. - About 73.6% of the free skate score is accounted for by the least-squares regression line with \( x = \) short program score. - About 73.6% of the variability in the free skate score is accounted for by the least-squares regression line with \( x = \) short program score. - There is a strong, positive, linear association between the free skate score and short program score. - About 73.6% of the variability in the short program score is accounted for by the least-squares regression line with \( x = \) free skate score.
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