In 2009, the New York Yankees won 103 baseball games during the regular season. The table on the next page lists the number of victories (W), the earned-run-average (ERA), and the batting average (AVG) of each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The batting average is one measure of effectiveness of the hitters, and a higher number is better. number of victories ( y) ERA ( X,) TEAM AVG (x2) New York Yankees 103 4.26 0.283 Los Angeles Angels 97 4.45 0.285 Boston Red Sox 95 4.35 0.270 Minnesota Twins Texas Rangers Detroit Tigers Seattle Mariners Tampa Bay Rays Chicago White Sox Toronto Blue Jays 87 4.50 0.274 87 4.38 0.260 86 4.29 0.260 85 3.87 0.258 84 4.33 0.263 79 4.14 0.258 75 4.47 0.266 Oakland Athletics 75 4.26 0.262 Cleveland Indians 65 5.06 0.264 Kansas City Royals 65 4.83 0.259 Baltimore Orioles 64 5.15 0.268 Using MINITAB PROGRAM and a = 0.05 to answer the following questions а. - Develop a correlation matrix. Indicate, interpret, and conduct the hypothesis testing of the coefficient of correlation between y and x,, y and x2, x,and x2. - Do you see any problems with multicollinearity? Explain. b. - Develop the best estimated regression equation. - Did the estimated regression equation provide a good fit to the data? Explain and given reasons to support your answer with assumption of residual and R2. - Indicate the best estimated regression equation and use it to predict the number of victories for a team if the earned-run-average is 4.75 and the batting average is 0.275?
In 2009, the New York Yankees won 103 baseball games during the regular season. The table on the next page lists the number of victories (W), the earned-run-average (ERA), and the batting average (AVG) of each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The batting average is one measure of effectiveness of the hitters, and a higher number is better. number of victories ( y) ERA ( X,) TEAM AVG (x2) New York Yankees 103 4.26 0.283 Los Angeles Angels 97 4.45 0.285 Boston Red Sox 95 4.35 0.270 Minnesota Twins Texas Rangers Detroit Tigers Seattle Mariners Tampa Bay Rays Chicago White Sox Toronto Blue Jays 87 4.50 0.274 87 4.38 0.260 86 4.29 0.260 85 3.87 0.258 84 4.33 0.263 79 4.14 0.258 75 4.47 0.266 Oakland Athletics 75 4.26 0.262 Cleveland Indians 65 5.06 0.264 Kansas City Royals 65 4.83 0.259 Baltimore Orioles 64 5.15 0.268 Using MINITAB PROGRAM and a = 0.05 to answer the following questions а. - Develop a correlation matrix. Indicate, interpret, and conduct the hypothesis testing of the coefficient of correlation between y and x,, y and x2, x,and x2. - Do you see any problems with multicollinearity? Explain. b. - Develop the best estimated regression equation. - Did the estimated regression equation provide a good fit to the data? Explain and given reasons to support your answer with assumption of residual and R2. - Indicate the best estimated regression equation and use it to predict the number of victories for a team if the earned-run-average is 4.75 and the batting average is 0.275?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Transcribed Image Text:In 2009, the New York Yankees won 103 baseball games during the regular season. The table on the next
page lists the number of victories (W), the earned-run-average (ERA), and the batting average (AVG) of
each team in the American League. The ERA is one measure of the effectiveness of the pitching staff, and a
lower number is better. The batting average is one measure of effectiveness of the hitters, and a higher
number is better.
中
number of victories (y)
ERA (x,)
TEAM
AVG (X2)
New York Yankees
103
4.26
0.283
Los Angeles Angels
97
4.45
0.285
Boston Red Sox
95
4.35
0.270
Minnesota Twins
87
4.50
0.274
Texas Rangers
Detroit Tigers
87
4.38
0.260
86
4.29
0.260
Seattle Mariners
85
3.87
0.258
Tampa Bay Rays
Chicago White Sox
Toronto Blue Jays
84
4.33
0.263
79
4.14
0.258
75
4.47
0.266
Oakland Athletics
75
4.26
0.262
Cleveland Indians
65
5.06
0.264
Kansas City Royals
65
4.83
0.259
Baltimore Orioles
64
5.15
0.268
Using MINITAB PROGRAM and a = 0.05 to answer the following questions
а.
- Develop a correlation matrix. Indicate, interpret, and conduct the hypothesis testing of the coefficient of
correlation between y and x,, y and x2, x,and x2.
- Do you see any problems with multicollinearity? Explain.
b.
- Develop the best estimated regression equation.
- Did the estimated regression equation provide a good fit to the data? Explain and given reasons to support
your answer with assumption of residual and R.
- Indicate the best estimated regression equation and use it to predict the number of victories for a team if the
earned-run-average is 4.75 and the batting average is 0.275?
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