Below are a randomly selected set of teams from Major League Baseball\'s American League. The team\'s batting average is linearly associated with the number of games won in a season. Hat y = -122.89011 + 746.03174(x), where x is the beam batting average; r = 0.674. What is the data\'s residual value for the team batting average of 0.271? What fraction of the variation in games won can be explained by the batting average and the linear model?
a).
Regression line
y = -122.89011+746.03174x
When x=0.271
y = -122.89011+746.03174*0.271 = 79.2845
observed y when x=0.271 is 80
residual = 80 - 79.2845 = 0.7155
b) r = 0.674
R2 =r*r=0.454276
Fraction of variation explained by the model = 0.454276
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