The Standard Error (highlighted in yellow in the Excel regression output) is used to calculate a confidence interval about the mean Y value. Fortunately there is an easy substitution that provides a fairly accurate estimate of Prediction Interval. Some software packages such as Minitab perform the internal calculations to produce an exact Prediction Error for a given Alpha.

This is given in Bowerman and O’Connell (1990).

Calculation of Distance value for any type of multiple regression requires some heavy-duty matrix algebra. Prediction Error = Standard Error of the Regression * SQRT(1 + distance value)ĭistance value, sometimes called leverage value, is the measure of distance of the combinations of values, x 1, x 2,…, x k from the center of the observed data. Prediction Interval = Y est ± t-Value α/2 * Prediction Error The formula for a prediction interval about an estimated Y value (a Y value calculated from the regression equation) is found by the following formula: Fortunately there is an easy short-cut that can be applied to multiple regression that will give a fairly accurate estimate of the prediction interval. There will always be slightly more uncertainty in predicting an individual Y value than in estimating the mean Y value.įor that reason, a Prediction Interval will always be larger than a Confidence Interval for any type of regression analysis.Ĭalculating an exact prediction interval for any regression with more than one independent variable (multiple regression) involves some pretty heavy-duty matrix algebra. The Prediction Error is use to create a confidence interval about a predicted Y value. The Standard Error of the Regression Equation is used to calculate a confidence interval about the mean Y value. The Prediction Error for a point estimate of Y is always slightly larger than the Standard Error of the Regression Equation shown in the Excel regression output directly under Adjusted R Square. A regression prediction interval is a value range above and below the Y estimate calculated by the regression equation that would contain the actual value of a sample with, for example, 95 percent certainty.

Regression - How To Do Conjoint Analysis Using Dummy Variable Regression in ExcelĪ prediction interval is a confidence interval about a Y value that is estimated from a regression equation. Normality Testing of Residuals in Excel 2010 and Excel 2013Įvaluating the Excel Output of Multiple RegressionĮstimating the Prediction Interval of Multiple Regression in Excel Multiple Linear Regression’s Required Residual Assumptions This is one of the following seven articles on Multiple Linear Regression in Excelīasics of Multiple Regression in Excel 2010 and Excel 2013Ĭomplete Multiple Linear Regression Example in 6 Steps in Excel 2010 and Excel 2013

Regression excel formula