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)
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)
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3SE: What is regression analysis? Describe the process of performing regression analysis on a graphing...
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![**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 (\(S_{\epsilon}\)) = 10.71
Calculate 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F136a9916-8a5d-490b-a1c4-57e644d5608a%2F24012ae9-79dd-45ea-879b-33c291ad3f9f%2Ffj6k9t9_processed.png&w=3840&q=75)
Transcribed Image Text:**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 (\(S_{\epsilon}\)) = 10.71
Calculate 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.
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