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:

Independent variable \(X\) sample data (comma or space separated) =
Dependent variable \(Y\) sample data (comma or space separated) =
Confidence Level (Ex: 0.95, 95, 99, 99%) =
X value for prediction \(X_0\) =
Independent variable Name (optional) =
Dependent variable Name (optional) =
 

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.




In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

log in

reset password

Back to
log in