One of the Most Frequently Used Summary Statistics for the Performance

Essay

One of the most frequently used summary statistics for the performance of a baseball
hitter is the so-called batting average.In essence, it calculates the percentage of hits in the
number of opportunities to hit (appearances "at the plate").The management of a
professional team has hired you to predict next season's performance of a certain hitter
who is up for a contract renegotiation after a particularly great year.To analyze the
situation, you search the literature and find a study which analyzed players who had at
least 50 at bats in 1998 and 1997.There were 379 such players.
(a)The reported regression line in the study is $$\widehat { \text { Batavg } _ { i } ^ { 1998 } } = 0.138 + 0.467 \times \text { Batavg } _ { i } ^ { 1997 } ; R ^ { 2 } = 0.17$$ and the intercept and slope are both statistically significant.What does the regression
imply about the relationship between past performance and present performance? What
values would the slope and intercept have to take on for the future performance to be as
good as the past performance, on average?