**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 information, given that Thus, the value of b is 0.5379. Obtain the value of a The value of a is obtained below: The formula to obtain a is, Thus, the value of a is 6.5644. Thus, the required regression equation is, (d) Predict the value of y for a successful field goals for a player with x=79 successful free throws. Sub x=79 in the regression equation. Thus, the predicted value of y for a successful field goals for a player with x=79 successful free throws is 49.06. (e) Obtain the 90% confidence interval for y when x=79. The 90% confidence interval for y when x=79 is obtained below as follows: The formula for the confidence interval is, Obtain the degrees of freedom. The degree of freedom is obtained below: Use EXCEL Procedure for finding the critical value of t. Follow the instruction to obtain the critical value of t: Open EXCEL Go to Formula bar. In formula bar enter the function as“=TINV” Enter the probability as 0.10. Enter the degrees of freedom as 4. Click enter. EXCEL output: From the EXCEL output, the critical value of t at the 0.10 level of significance with the 4 degrees of freedom is 2.131847. The required CI is, The 90% confidence interval for y when x=79 is between 45.5 and 52.6. Lower limit is 45.5% Upper limit is 52.6%.

Math

Statistics

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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