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worse than average, in the second. Find the predicted second-round score for a player who shot 80 in the first round. Give your answer to two decimal places. predicted score: Find the predicted second-round score for a player who shot 70 in the first round. Give your answer to two decimal places. predicted score: (Comment: This is regression to the mean. If you select individuals with extreme scores on some measure, they tend to have less extreme scores when measured again. That's because their extreme position is partly merit and partly luck, and the luck will be different next time. Regression to the mean contributes to lots of "effects". The rookie of the year often doesn't do as well the next year; the best player in an orchestral audition may play less well once hired than the runners-up; a student who feels she needs coaching after the SAT often does better on the next try without coaching.)

worse than average, in the second. Find the predicted second-round score for a player who shot 80 in the first round. Give your answer to two decimal places. predicted score: Find the predicted second-round score for a player who shot 70 in the first round. Give your answer to two decimal places. predicted score: (Comment: This is regression to the mean. If you select individuals with extreme scores on some measure, they tend to have less extreme scores when measured again. That's because their extreme position is partly merit and partly luck, and the luck will be different next time. Regression to the mean contributes to lots of "effects". The rookie of the year often doesn't do as well the next year; the best player in an orchestral audition may play less well once hired than the runners-up; a student who feels she needs coaching after the SAT often does better on the next try without coaching.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The image illustrates the relationship between golfers' scores on the first and second rounds of the 2019 Masters Tournament. **Scatter Plot:** - **X-Axis (Horizontal):** Represents the first-round scores, ranging from 65 to 85. - **Y-Axis (Vertical):** Represents the second-round scores, ranging from 65 to 80. - Each point on the graph indicates a player's first-round score against their second-round score. **Analysis:** - **Least-Squares Line Equation:** \( \hat{y} = 62.91 + 0.164x \) - This equation predicts the second-round scores (\( \hat{y} \)) based on the first-round scores (\( x \)). - **Mean Second-Round Score:** 75.02 - Players who perform well in the first round are predicted to score worse than their first round in the second round, though better than average. Conversely, players who do poorly in the first round are predicted to improve, but still score worse than average, in the second round. **Example Task:** - **Prediction:** Find the predicted second-round score for a player who scored 80 in the first round. The task involves substituting the first-round score (80) into the least-squares line equation to calculate the predicted second-round score.
Transcribed Image Text:The image illustrates the relationship between golfers' scores on the first and second rounds of the 2019 Masters Tournament. **Scatter Plot:** - **X-Axis (Horizontal):** Represents the first-round scores, ranging from 65 to 85. - **Y-Axis (Vertical):** Represents the second-round scores, ranging from 65 to 80. - Each point on the graph indicates a player's first-round score against their second-round score. **Analysis:** - **Least-Squares Line Equation:** \( \hat{y} = 62.91 + 0.164x \) - This equation predicts the second-round scores (\( \hat{y} \)) based on the first-round scores (\( x \)). - **Mean Second-Round Score:** 75.02 - Players who perform well in the first round are predicted to score worse than their first round in the second round, though better than average. Conversely, players who do poorly in the first round are predicted to improve, but still score worse than average, in the second round. **Example Task:** - **Prediction:** Find the predicted second-round score for a player who scored 80 in the first round. The task involves substituting the first-round score (80) into the least-squares line equation to calculate the predicted second-round score.
### Regression to the Mean: Predicted Second-Round Scores #### Task Find the predicted second-round score for a player who shot 80 in the first round. Give your answer to two decimal places. - **Predicted Score:** [Input Box] Find the predicted second-round score for a player who shot 70 in the first round. Give your answer to two decimal places. - **Predicted Score:** [Input Box] #### Explanation of Concept **Regression to the Mean** If you select individuals with extreme scores on some measure, they tend to have less extreme scores when measured again. This is because their extreme position is partly due to merit and partly due to luck, and the luck will vary next time. This concept explains many observed phenomena: - The "rookie of the year" often underperforms in the following year. - The best player in an orchestral audition may not perform as well once hired compared to the runners-up. - A student feeling the need for coaching after a test often improves naturally on the next attempt without additional help. Understanding regression to the mean is crucial for interpreting scores and outcomes accurately across various fields.
Transcribed Image Text:### Regression to the Mean: Predicted Second-Round Scores #### Task Find the predicted second-round score for a player who shot 80 in the first round. Give your answer to two decimal places. - **Predicted Score:** [Input Box] Find the predicted second-round score for a player who shot 70 in the first round. Give your answer to two decimal places. - **Predicted Score:** [Input Box] #### Explanation of Concept **Regression to the Mean** If you select individuals with extreme scores on some measure, they tend to have less extreme scores when measured again. This is because their extreme position is partly due to merit and partly due to luck, and the luck will vary next time. This concept explains many observed phenomena: - The "rookie of the year" often underperforms in the following year. - The best player in an orchestral audition may not perform as well once hired compared to the runners-up. - A student feeling the need for coaching after a test often improves naturally on the next attempt without additional help. Understanding regression to the mean is crucial for interpreting scores and outcomes accurately across various fields.
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