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The accompanying data are the number of wins and the earmed run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins E Click the icon to view the table of numbers of wins and earned run average. (b) x= 10 wins (c) x= 19 wins (d) x= 15 wins Wins and ERA The equation of the regression line is y =x+ (Round to two decimal places as needed.) Construct a scatter plot of the data and draw the regression line. Choose Earned run O A. OB. Wins, x average, y 2.82 AERA 6- AERA 20 18 3.34 4- 4- 17 2.59 16 3.72 2- 2- 14 3.85 0- 12 4.31 12 18 24 12 18 24 Wins 11 3.81 Wins 5.05 (a) Predict the ERA for 5 wins, if it is meaningful. Select the correct choid O A. y= (Round to two decimal places as needed.) Print Done It in not moaningfiol to prodint thic valun of u hnun v-E ie not Next

The accompanying data are the number of wins and the earmed run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=5 wins E Click the icon to view the table of numbers of wins and earned run average. (b) x= 10 wins (c) x= 19 wins (d) x= 15 wins Wins and ERA The equation of the regression line is y =x+ (Round to two decimal places as needed.) Construct a scatter plot of the data and draw the regression line. Choose Earned run O A. OB. Wins, x average, y 2.82 AERA 6- AERA 20 18 3.34 4- 4- 17 2.59 16 3.72 2- 2- 14 3.85 0- 12 4.31 12 18 24 12 18 24 Wins 11 3.81 Wins 5.05 (a) Predict the ERA for 5 wins, if it is meaningful. Select the correct choid O A. y= (Round to two decimal places as needed.) Print Done It in not moaningfiol to prodint thic valun of u hnun v-E ie not Next

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Transcription and Explanation for Educational Use** The image contains a task related to regression analysis in the context of baseball statistics. It involves the following elements: 1. **Problem Statement:** - The accompanying data represents the number of wins and the earned run averages (ERA) for eight baseball pitchers in a recent season. - The task is to find the equation of the regression line and use it to predict the ERA for given win values. - There’s a specific focus on whether predictions are meaningful for certain values of wins. 2. **Equation of the Regression Line:** - The general form of the equation provided is \( \hat{y} = \_ x + \_ \). - Students are required to fill in the blanks and round their answers to two decimal places as needed. 3. **Scatter Plot and Regression Line:** - Students must construct a scatter plot of the data and draw the regression line, choosing the correct graph from the given options: - **Graph A:** - Shows a downward trend with data points tightly clustered around a downward-sloping line. - **Graph B:** - Similar downward trend but the line is less steep and data points are more spread out. - **Graph C and D:** - Continue the pattern of negative correlation but differ in slope steepness and point distribution. 4. **ERA Prediction:** - The step asks for the prediction of ERA for 5 wins. - Options include: - Calculating \( \hat{y} \) with required precision. - Indicating the prediction might be meaningless due to missing \( x \)-value from original data. 5. **Additional Notes:** - Graph analysis involves assessing which plot accurately represents the regression line with the scatter of given data. - Concepts checked include understanding regression interpretation, scatter plot analysis, and meaningfulness of predictions based on data availability. This explanation provides a backdrop for understanding statistical analysis using regression, focusing on practical applications within sports analytics.
Transcribed Image Text:**Transcription and Explanation for Educational Use** The image contains a task related to regression analysis in the context of baseball statistics. It involves the following elements: 1. **Problem Statement:** - The accompanying data represents the number of wins and the earned run averages (ERA) for eight baseball pitchers in a recent season. - The task is to find the equation of the regression line and use it to predict the ERA for given win values. - There’s a specific focus on whether predictions are meaningful for certain values of wins. 2. **Equation of the Regression Line:** - The general form of the equation provided is \( \hat{y} = \_ x + \_ \). - Students are required to fill in the blanks and round their answers to two decimal places as needed. 3. **Scatter Plot and Regression Line:** - Students must construct a scatter plot of the data and draw the regression line, choosing the correct graph from the given options: - **Graph A:** - Shows a downward trend with data points tightly clustered around a downward-sloping line. - **Graph B:** - Similar downward trend but the line is less steep and data points are more spread out. - **Graph C and D:** - Continue the pattern of negative correlation but differ in slope steepness and point distribution. 4. **ERA Prediction:** - The step asks for the prediction of ERA for 5 wins. - Options include: - Calculating \( \hat{y} \) with required precision. - Indicating the prediction might be meaningless due to missing \( x \)-value from original data. 5. **Additional Notes:** - Graph analysis involves assessing which plot accurately represents the regression line with the scatter of given data. - Concepts checked include understanding regression interpretation, scatter plot analysis, and meaningfulness of predictions based on data availability. This explanation provides a backdrop for understanding statistical analysis using regression, focusing on practical applications within sports analytics.
### Understanding Wins and Earned Run Averages (ERA) with Regression Analysis The problem involves analyzing the number of wins and the earned run averages (ERA) of eight baseball pitchers in a recent season. The task is to find the equation of the regression line and construct a scatter plot to understand the relationship between wins and ERA. #### Data Table The table titled "Wins and ERA" provides the following data: - **Wins (x):** 20, 18, 17, 16, 14, 12, 11, 9 - **Earned Run Average (y):** 2.82, 3.34, 2.59, 3.72, 3.85, 4.31, 3.81, 5.05 #### Regression Line - **Equation of Regression Line:** The equation to be found is of the form \( \hat{y} = b_0 + b_1x \), where \( \hat{y} \) is the predicted ERA, \( b_0 \) is the y-intercept, and \( b_1 \) is the slope. - The regression line will be calculated, rounding to two decimal places as needed. #### Scatter Plots Two possible scatter plots are shown: - **Option A:** Features a plot that displays data points with a negative slope fitting the observed data points. - **Option B:** A similar negative slope but different positioning or scale. Each plot has: - **X-axis:** Number of Wins - **Y-axis:** Earned Run Average (ERA) The task is to choose the scatter plot that best represents the data and ensure the regression line fits well. #### Predicting ERA - **Prediction for 5 Wins:** An evaluation is to be made on whether it is meaningful to predict ERA for 5 wins using the regression model. - **Option A:** Calculates \( \hat{y} \) and rounds to two decimal places if meaningful. - **Option B:** Determines if predicting for 5 wins is not meaningful due to it being beyond the reasonable range of the data. This problem involves interpreting statistical data and applying regression analysis to make informed predictions.
Transcribed Image Text:### Understanding Wins and Earned Run Averages (ERA) with Regression Analysis The problem involves analyzing the number of wins and the earned run averages (ERA) of eight baseball pitchers in a recent season. The task is to find the equation of the regression line and construct a scatter plot to understand the relationship between wins and ERA. #### Data Table The table titled "Wins and ERA" provides the following data: - **Wins (x):** 20, 18, 17, 16, 14, 12, 11, 9 - **Earned Run Average (y):** 2.82, 3.34, 2.59, 3.72, 3.85, 4.31, 3.81, 5.05 #### Regression Line - **Equation of Regression Line:** The equation to be found is of the form \( \hat{y} = b_0 + b_1x \), where \( \hat{y} \) is the predicted ERA, \( b_0 \) is the y-intercept, and \( b_1 \) is the slope. - The regression line will be calculated, rounding to two decimal places as needed. #### Scatter Plots Two possible scatter plots are shown: - **Option A:** Features a plot that displays data points with a negative slope fitting the observed data points. - **Option B:** A similar negative slope but different positioning or scale. Each plot has: - **X-axis:** Number of Wins - **Y-axis:** Earned Run Average (ERA) The task is to choose the scatter plot that best represents the data and ensure the regression line fits well. #### Predicting ERA - **Prediction for 5 Wins:** An evaluation is to be made on whether it is meaningful to predict ERA for 5 wins using the regression model. - **Option A:** Calculates \( \hat{y} \) and rounds to two decimal places if meaningful. - **Option B:** Determines if predicting for 5 wins is not meaningful due to it being beyond the reasonable range of the data. This problem involves interpreting statistical data and applying regression analysis to make informed predictions.
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