The data below represent the number of wins by 11 major league baseball teams and the team ERA. The owners would like to know if there is a linear relationship between the team ERA (earned run average) and the number of wins in a season. Using the data given, answer the questions below: Team ERA Wins Chicago White Sox 4.4 62 Chicago Cubs 4.8 102 Cleveland Guardians 8.6 50 Cincinnati Reds 6.4 84 Detroit Tigers 14.9 60 Milwaukee Brewers 3.3 135 Kansas City Royals 8.2 59 Pittsburgh Pirates 7.8 58 Minnesota Twins 4.5 105 St. Louis Cardinals 6.7 82 New York Yankees 5.4 95 a. Develop the least squares regression equation. b. Estimate the number of wins for a team with a 6.0 ERA. c. Compute the coefficient of determination. Explain what this means in your own words in the context of the problem. d. Using a t test, complete a hypothesis test to determine whether the slope is significantly different from zero. Let α = .05. Explain what this means in the context of the problem. e. Develop a 95% prediction interval for a team with a 6.0 ERA. f. Compute the leverage values for these data. What leverage value would be defined to be "high leverage?" Do there appear to be any influential observations - i.e. high leverage points- in these data? Explain. g. Compute the standardized residuals for these data. Do the data include any outliers? Explain
The data below represent the number of wins by 11 major league baseball teams and the team ERA. The owners would like to know if there is a linear relationship between the team ERA (earned run average) and the number of wins in a season. Using the data given, answer the questions below:
|
Team |
ERA |
Wins |
|
Chicago White Sox |
4.4 |
62 |
|
Chicago Cubs |
4.8 |
102 |
|
Cleveland Guardians |
8.6 |
50 |
|
Cincinnati Reds |
6.4 |
84 |
|
Detroit Tigers |
14.9 |
60 |
|
Milwaukee Brewers |
3.3 |
135 |
|
Kansas City Royals |
8.2 |
59 |
|
Pittsburgh Pirates |
7.8 |
58 |
|
Minnesota Twins |
4.5 |
105 |
|
St. Louis Cardinals |
6.7 |
82 |
|
New York Yankees |
5.4 |
95 |
|
|
|
b. Estimate the number of wins for a team with a 6.0 ERA. |
|
c. Compute the coefficient of determination. Explain what this means in your own words in the context of the problem. |
|
d. Using a t test, complete a hypothesis test to determine whether the slope is significantly different from zero. Let α = .05. Explain what this means in the context of the problem. |
|
e. Develop a 95% prediction interval for a team with a 6.0 ERA. |
|
f. Compute the leverage values for these data. What leverage value would be defined to be "high leverage?" Do there appear to be any influential observations - i.e. high leverage points- in these data? Explain. |
|
g. Compute the standardized residuals for these data. Do the data include any outliers? Explain. |
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The data below represent the number of wins by 11 major league baseball teams and the team ERA. The owners would like to know if there is a linear relationship between the team ERA (earned run average) and the number of wins in a season. Using the data given, answer the questions below:
|
Team |
ERA |
Wins |
|
Chicago White Sox |
4.4 |
62 |
|
Chicago Cubs |
4.8 |
102 |
|
Cleveland Guardians |
8.6 |
50 |
|
Cincinnati Reds |
6.4 |
84 |
|
Detroit Tigers |
14.9 |
60 |
|
Milwaukee Brewers |
3.3 |
135 |
|
Kansas City Royals |
8.2 |
59 |
|
Pittsburgh Pirates |
7.8 |
58 |
|
Minnesota Twins |
4.5 |
105 |
|
St. Louis Cardinals |
6.7 |
82 |
|
New York Yankees |
5.4 |
95 |
|
|
|
b. Estimate the number of wins for a team with a 6.0 ERA. |
|
c. Compute the coefficient of determination. Explain what this means in your own words in the context of the problem. |
|
d. Using a t test, complete a hypothesis test to determine whether the slope is significantly different from zero. Let α = .05. Explain what this means in the context of the problem. |
|
e. Develop a 95% prediction interval for a team with a 6.0 ERA. |
|
f. Compute the leverage values for these data. What leverage value would be defined to be "high leverage?" Do there appear to be any influential observations - i.e. high leverage points- in these data? Explain. |
|
g. Compute the standardized residuals for these data. Do the data include any outliers? Explain. |
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