To find the 95% confidence interval for the slope of a simple linear regression model, you typically need the point estimate (the slope), the standard error of the slope, and the appropriate t-value from the t-distribution for n-2 degrees of freedom (where n is the number of data points).
Given that you mentioned n = 20, this would imply there are 18 degrees of freedom (df = n - 2 = 20 - 2).
The formula for the confidence interval for the slope (β) is given by:
\[ \beta \pm t_{\alpha/2} \cdot SE(\beta) \]
Where:
- \( \beta \) is the estimate of the slope,
- \( t_{\alpha/2} \) is the t-value for a two-tailed test at df degrees of freedom with the desired level of confidence,
- \( SE(\beta) \) is the standard error of the slope.
To find the correct 95% confidence interval among the options provided, we typically need to see the point estimate (slope) and its standard error or a context in which these values have been calculated.
Without this specific information, I cannot calculate or verify which of the intervals you provided is correct based on the mathematical approach. However, you can check the values provided with typical confidence interval calculations, or you can look up the t-value for 18 degrees of freedom at a 95% confidence level, which is roughly 2.101, and calculate the confidence intervals if you determine the slope and its standard error.
With just the provided intervals:
- [10.3767; 10.8233]
- [3.1830; 3.6171]
- [1.1381; 5.6619]
- [2.9430; 3.8570]
- [3.1907; 3.6093]
If the slope estimate and its standard error were known, you would substitute them into the formula to check which interval correctly represents the 95% confidence interval for the slope of your regression analysis.
Please provide the slope estimate and its standard error if available, to determine the correct confidence interval.
1 answer