Confidence Interval Calculator for a Regression Prediction
Instructions: Use this confidence interval calculator for the mean response of a regression prediction. Please input the data for the independent variable \((X)\) and the dependent variable (\(Y\)), the confidence level and the X-value for the prediction, in the form below:
Confidence Interval for the Mean Response
The Confidence Interval for the Mean Response corresponds to the calculated confidence interval for the mean predicted response \(\mu_{Y|X_0}\) for a given value \(X = X_0\). First, we need to know the mean squared error:
\[\hat{\sigma}^2 = \displaystyle \frac{SSE}{n-2}\]Then, the \(1-\alpha)\times 100 \)% confidence interval for the mean response \(\mu_{Y|X_0}\) is
\[CI = \displaystyle \left( \hat\mu_{Y|X_0} - t_{\alpha/2; n-2} \sqrt{ \hat{\sigma}^2 \left(\frac{1}{n} + \frac{\left(X_0 - \bar X\right)^2}{SS_{XX}}\right) }, \hat\mu_{Y|X_0} + t_{\alpha/2; n-2} \sqrt{ \hat{\sigma}^2 \left(\frac{1}{n} + \frac{\left(X_0 - \bar X\right)^2}{SS_{XX}}\right) } \right)\]If you are interested rather in a confidence interval for the prediction itself, please use instead this prediction interval calculator for regression predictions .
