In 2001, the Arizona Diamondbacks Defeated the New York Yankees

question 16

Essay

In 2001, the Arizona Diamondbacks defeated the New York Yankees in the Baseball
World Series in 7 games.Some players, such as Bautista and Finley for the
Diamondbacks, had a substantially higher batting average during the World Series than
during the regular season.Others, such as Brosius and Jeter for the Yankees, did
substantially poorer.You set out to investigate whether or not the regular season batting
average is a good indicator for the World Series batting average.The results for 11
players who had the most at bats for the two teams are: $$\begin{array} { l } \widehat { A Z W \text { savg } } = - 0.347 + 2.290 \text { AZSeasavg } , R ^ { 2 } = 0.11 , \text { SER } = 0.145 , \\\\\widehat { N Y W \text { savg } } = 0.134 + 0.136 \text { NYSeasavg } , R ^ { 2 } = 0.001 , \text { SER } = 0.092 ,\end{array}$$ where Wsavg and Seasavg indicate the batting average during the World Series and the
regular season respectively.
(a)Focusing on the coefficients first, what is your interpretation?

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Definitions:

Addition Law

In probability, the rule that calculates the probability of the occurrence of at least one of two events.

Binomial Distribution

A probability distribution that summarizes the likelihood that a value will take one of two independent states under a given set of parameters or conditions.

Negatively Skewed

Negatively skewed, in statistics, describes a distribution of data where the tail is longer on the left side of the distribution curve, indicating that the bulk of the values lie to the right.

Positively Skewed

A statistical distribution characterized by a longer tail on the right side, indicating that the bulk of the values lie to the left of the mean.