Solvers Statistics

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 .