**Educational Website Content: Statistical Analysis of Basketball Player Performance**---**Introduction**In this section, we explore the relationship between free throw and field goal success rates among professional basketball players. We use statistical methods to analyze data from a random sample of players.**Data Summary**Let \( x \) be a random variable representing the percentage of successful free throws a professional basketball player makes in a season. Let \( y \) represent the percentage of successful field goals made in a season. A random sample of \( n = 6 \) players yielded the following data:| \( x \) | 67 | 64 | 75 | 86 | 73 | 73 ||---------|----|----|----|----|----|----|| \( y \) | 42 | 39 | 48 | 51 | 44 | 51 |**Statistical Information**- \(\Sigma x = 438\)- \(\Sigma y = 275\)- \(\Sigma x^2 = 32264\)- \(\Sigma y^2 = 12727\)- \(\Sigma xy = 20231\)- \( r \approx 0.827 \)**Analysis Tasks****(d) Predicted Successful Field Goals**To find the predicted percentage (\( \hat{y} \)) of successful field goals for a player with \( x = 79\% \) successful free throws, the linear regression equation would be applied. Round your answer to two decimal places.Predicted \( \hat{y} \): [Input your solution]**(e) Confidence Interval Calculation**Determine the 90% confidence interval for \( y \) when \( x = 79 \). Round your answers to one decimal place.- Lower Limit: [Input your solution] %- Upper Limit: [Input your solution] %**Conclusion**This example illustrates the use of correlation and regression analysis to predict player performance based on historical data. Participants are encouraged to conduct similar analyses on additional data sets to gain deeper insights into sports analytics.--- **Note**: Calculations are to be filled out using appropriate statistical formulas based on the data summary provided.

(d) Obtain the value of b(slope) The value of slope is obtained below as follows: From the…

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. 73 73 67 42 64 39 75 48 86 51 44 51 Ex = 438, Ey = 275, Ex² = 32264, Ey² = 12727, Exy = 20231, and r= 0.827. (d) Find the predicted percentage ŷ of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.) lower limit upper limit %

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. 73 73 67 42 64 39 75 48 86 51 44 51 Ex = 438, Ey = 275, Ex² = 32264, Ey² = 12727, Exy = 20231, and r= 0.827. (d) Find the predicted percentage ŷ of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.) lower limit upper limit %

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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