**Title: Understanding Confidence Intervals in Regression Analysis****Introduction**In regression analysis, understanding confidence intervals for predicted values is crucial for interpreting the reliability of predictions. Below is a demonstration of calculating a 90% confidence interval for a given scenario.**Problem Statement**Given the regression equation:\[ \hat{y} = 5.23 + 2.78x \]Parameters:- n (sample size) = 24- Mean of x (\(\bar{x}\)) = 12.56- Standard deviation of x (\(s_{x}\)) = 5.87- Standard error (\(S_{\epsilon}\)) = 10.71Calculate the 90% confidence interval for \( \hat{y} \) when \( x = 11 \).**Options:**- (2.74, 5.23)- (16.21, 54.53)- (20.30, 40.74)- (35.37, 70.74)- (12.56, 55.87)**Conclusion & Explanation**To determine the correct confidence interval, it's necessary to plug in the provided values into the appropriate statistical formulas. The process involves:1. Computing the predicted value (\(\hat{y}\)).2. Calculating the margin of error using the t-score corresponding to a 90% confidence level and the provided standard error (\(S_{\epsilon}\)).3. Adding and subtracting this margin of error from the predicted value to get the confidence interval.By analyzing and understanding these steps, one can identify the correct confidence interval for predictions based on the regression model.

Answered: In the regression equation -5.23 2.74x…

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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In the regression equation -5.23 2.74x and n-24, the mean of x is 1256, 55-55.87 and 5-1071. A 90% confidence interval for y when x-11 is, O (2.74,523) O (16.21, 54.531 (30.00,40.74) O (35.37, 70.741 O [12.56, 55.87)