The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect (i) a good pitching staff and (ii) a good team defense. You are to investigate the relationship between a team's winning percentage - Y, and its Earned Run Average (ERA) - X.
The following data represents the winning percentage (the number of wins out of 162 games in a season) as well as the teams Earned Run Average, or ERA.
The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect (i) a good pitching staff and (ii) a good team defense. You are to investigate the relationship between a team's winning percentage - Y, and its Earned Run Average (ERA) - X.
| Winning Proportion - Y | Earned Run Average (ERA) - X |
| 0.623457 | 3.13 |
| 0.512346 | 3.97 |
| 0.635802 | 3.68 |
| 0.604938 | 3.92 |
| 0.518519 | 4.00 |
| 0.580247 | 4.12 |
| 0.413580 | 4.29 |
| 0.407407 | 4.62 |
| 0.462963 | 3.89 |
| 0.450617 | 5.20 |
| 0.487654 | 4.36 |
| 0.456790 | 4.91 |
| 0.574047 | 3.75 |
(b) Use R-Studio to find the least squares estimate of the linear model that expressed a teams winning percentage as a linear
Y^i = ? + - Xi
(e) A certain professional baseball team had an earned run average of 3.45 this past season. How many games out of 162 would you expect this team to win? Use two decimals in your answer.
games won
(f) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer.
ei=
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
