Question

Which team statistic is the best variable to use to predict a team's winning percentage? One pitching, one fielding, and one hitting statistic was measured for each major league baseball team at the end of the 2019 season. The dataset is called "2019 MLB Team Statistics. The three explanatory variables as follows. Earned Run Average (ERA): a pitching statistic Fielding %: a fielding statistic Home Runs: a hitting statistic Wis Loss Win Loss 054 Eamed Run Arome 0978 09892098409609 Fielding 300 Correlation matrix: Win Loss % Earned Run Average Fielding % Home Runs -0.83399384 10.32183594 0.76281516 Which explanatory variable has the strongest relationship with the response variable and a reason why in a complete sentence? Interpret the scatterplot of ERA and Win-Loss % in terms of trend, strength, and shape (form) in one complete sentence. Simple linear regression results: Dependent Variable: Win Loss % Independent Variable: Earned Run Average Win-Loss % -1.1309735 -0.1403247 Earned Run Average Sample size: 30 R (correlation coefficient) = -0.83399384R-sg-0.69554573 Estimate of error standard deviation: 0.055008616 Eamed Run Average b. c. d. Type the regression equation and Interpret the slope of the regression line (in context of this data set). Is it meaningful to interpret they intercept? Why or why not? Stater-squared Gic., the coefficient of determination) and explain what this value means in context of the data set. Use the regression equation from part (c) to predict a random team's Win Loss % for when their ERA is 7.00. State your predicted value in a sentence that is in context of the data. Is your prediction in part (k) an example of extrapolation? Why or why not?

Answer 1

a)
Earned Run average has strongest relationship as its has greatest absolute correlation

there is negative , strong correlation

b)
y^ = 1.13097 - 0.1403247 ERA

slope = -0.1403
it means when earned run average increases by 1 units, on average win-loss % decreases by 0.14

y-intercept should not be interpreted as there is no 0 ERA in sample
c)
r^2 = 0.6955
it means 69.55 % of variation in WIn-Loss% is explained by ERA

d)
ERA = 7
y^ = 1.13097 - 0.1403247 *7
= 0.14869

yes, this is extrapolation , as 7 is not present in sample

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