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 (a) Find the least squares estimate of the linear model that expressed a teams winning percentage as a linear function of is ERA. Use four decimals in each of your answers. Y^i = __________ +/- _________________Xi (b) Find the value of the coefficient of determination, then complete its interpretation. r2= ___________ (use four decimals) The percentage of A. Variation B. Standard deviation C. The mean in A. a teams earned run average B. A teams winning percentage that is explained by its linear relationship with A. a teams earned run average B. A teams winning percentage is ___________ %. (c) 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 (d) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer. ei = _____________
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 |
(a) Find the least squares estimate of the linear model that expressed a teams winning percentage as a linear
Y^i = __________ +/- _________________Xi
(b) Find the value of the coefficient of determination, then complete its interpretation.
r2= ___________ (use four decimals)
The percentage of
A. Variation
B. Standard deviation
C. The mean
in
A. a teams earned run average
B. A teams winning percentage
that is explained by its linear relationship with
A. a teams earned run average
B. A teams winning percentage
is
(c) 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
(d) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer.
ei = _____________
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