Question

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)** Using MINITAB, create a scatter-plot of the
data. What can you conclude from this scatter-plot?

**A.** There is a negative linear relationship between
a teams winning percentage and its ERA.

**B.** There is not a linear relationship between the
a teams winning percentage and its ERA.

**C.** There is a positive linear relationship between
a teams winning percentage and its ERA.

**(b)** Use MINITAB to 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.

?ˆ?= ______ +/- _______ ??

**(c)** Find the value of the coefficient of
determination, then complete its interpretation.

?2= ______ (use four decimals)

The percentage of ? variation standard deviation the
mean in ? a teams winning percentage a teams
earned run average that is explained by its linear
relationship with ? the teams winning percentage the
teams earned run average is ________ %.

**(d)** Interpret the meaning of the slope term in the
estimate of the linear model, in the context of the
data.

As a teams ? winning percentage earned run
average increases by ? one percentage point
one earned run the teams ? winning percentage
earned run average will ? will increase by an
average of will decrease by an average of will increase by will
decrease by _______ . (use four decimals)

**(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.

??= ________

Answer #1

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sample of 10 NFL teams for the 2011 season (NFL website, February
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The accompanying data are the number of wins and the earned run
averages (mean number of earned runs allowed per nine innings
pitched) for
eight
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regression line. Then construct a scatter plot of the data and draw
the regression line. Then use the regression equation to predict
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comprises 162 games). Then multiply by 2 because there are two
teams in each game. Use the Poisson distribution to estimate the
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The National Football League (NFL) records a variety of
performance data for individuals and teams. To investigate the
importance of passing on the percentage of games won by a team, the
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Excel File
https://drive.google.com/file/d/1pfIsW3U477qRB8nj0fv_PD1fnRHV68Xx/view?usp=sharing
(a)
Using Excel Regression Analysis, write...

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