Major League Baseball (MLB) consists of 30 The earned run average, ERA, is a statistic used to measure a pitcher's (the person who throws the ball to the person trying to hit the ball) effectiveness. The lower the ERA, the more effective the pitcher is. Statisticians are trying to show there is a correlation between the team’s ERA and the number of wins. The data on the spreadsheet is from all the teams in the 2021 regular season. Find the equation for the regression line for this data. Find the correlation coefficient and R2. State the Null and Alternate Hypothesis. State Decision Rule and Critical Value at the 5% significance level (think about whether this should be a one or two tailed test and which test statistic needs to be calculated). Compute the test statistic and p-value. What is your decision concerning Null? What does that mean? If the ERA were 4.5, what is the predicted number of wins (ŷ) using the regression line? ERA to wins in 2021 (n = 30) ERA (X) Wins (Y) 1 3.01 106 2 3.24 107 3 3.50 95 4 3.67 100 5 3.73 93 6 3.74 92 7 3.78 95 8 3.88 88 9 3.90 77 10 3.91 91 11 3.96 67 12 3.98 90 13 4.02 86 14 4.10 79 15 4.26 92 16 4.30 90 17 4.32 77 18 4.34 80 19 4.39 82 20 4.40 83 21 4.64 74 22 4.69 77 23 4.79 60 24 4.80 65 25 4.82 74 26 4.83 73 27 4.87 71 28 5.08 61 29 5.11 52 30 5.84 52
Major League Baseball (MLB) consists of 30 The earned run average, ERA, is a statistic used to measure a pitcher's (the person who throws the ball to the person trying to hit the ball) effectiveness. The lower the ERA, the more effective the pitcher is. Statisticians are trying to show there is a correlation between the team’s ERA and the number of wins. The data on the spreadsheet is from all the teams in the 2021 regular season. Find the equation for the regression line for this data. Find the correlation coefficient and R2. State the Null and Alternate Hypothesis. State Decision Rule and Critical Value at the 5% significance level (think about whether this should be a one or two tailed test and which test statistic needs to be calculated). Compute the test statistic and p-value. What is your decision concerning Null? What does that mean? If the ERA were 4.5, what is the predicted number of wins (ŷ) using the regression line? ERA to wins in 2021 (n = 30) ERA (X) Wins (Y) 1 3.01 106 2 3.24 107 3 3.50 95 4 3.67 100 5 3.73 93 6 3.74 92 7 3.78 95 8 3.88 88 9 3.90 77 10 3.91 91 11 3.96 67 12 3.98 90 13 4.02 86 14 4.10 79 15 4.26 92 16 4.30 90 17 4.32 77 18 4.34 80 19 4.39 82 20 4.40 83 21 4.64 74 22 4.69 77 23 4.79 60 24 4.80 65 25 4.82 74 26 4.83 73 27 4.87 71 28 5.08 61 29 5.11 52 30 5.84 52
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 15PPS
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- Major League Baseball (MLB) consists of 30 The earned run average, ERA, is a statistic used to measure a pitcher's (the person who throws the ball to the person trying to hit the ball) effectiveness. The lower the ERA, the more effective the pitcher is. Statisticians are trying to show there is a
correlation between the team’s ERA and the number of wins. The data on the spreadsheet is from all the teams in the 2021 regular season.- Find the equation for the regression line for this data.
- Find the
correlation coefficient and R2. - State the Null and Alternate Hypothesis.
- State Decision Rule and Critical Value at the 5% significance level (think about whether this should be a one or two tailed test and which test statistic needs to be calculated).
- Compute the test statistic and p-value.
- What is your decision concerning Null? What does that mean?
- If the ERA were 4.5, what is the predicted number of wins (ŷ) using the regression line?
| ERA to wins in 2021 (n = 30) | ||||||||
| ERA (X) | Wins (Y) |
|
||||||
| 1 | 3.01 | 106 | ||||||
| 2 | 3.24 | 107 | ||||||
| 3 | 3.50 | 95 | ||||||
| 4 | 3.67 | 100 | ||||||
| 5 | 3.73 | 93 | ||||||
| 6 | 3.74 | 92 | ||||||
| 7 | 3.78 | 95 | ||||||
| 8 | 3.88 | 88 |
|
|||||
| 9 | 3.90 | 77 | ||||||
| 10 | 3.91 | 91 | ||||||
| 11 | 3.96 | 67 | ||||||
| 12 | 3.98 | 90 | ||||||
| 13 | 4.02 | 86 | ||||||
| 14 | 4.10 | 79 | ||||||
| 15 | 4.26 | 92 | ||||||
| 16 | 4.30 | 90 | ||||||
| 17 | 4.32 | 77 | ||||||
| 18 | 4.34 | 80 | ||||||
| 19 | 4.39 | 82 | ||||||
| 20 | 4.40 | 83 | ||||||
| 21 | 4.64 | 74 | ||||||
| 22 | 4.69 | 77 | ||||||
| 23 | 4.79 | 60 | ||||||
| 24 | 4.80 | 65 | ||||||
| 25 | 4.82 | 74 | ||||||
| 26 | 4.83 | 73 | ||||||
| 27 | 4.87 | 71 | ||||||
| 28 | 5.08 | 61 | ||||||
| 29 | 5.11 | 52 | ||||||
| 30 | 5.84 | 52 |
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