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Design of Experiments Guide > Technical Details > Relative Prediction Variance
Publication date: 04/21/2023

Relative Prediction Variance

The calculation of the relative prediction variance for a designed experiment is provided below. Consider the following notation:

X

Model matrix. See Model Matrix. Custom designs provide a script that shows the model matrix. See Save X Matrix.

σ2

Error variance.

Equation shown here

Vector of least squares estimates of the parameters.

Equation shown here

The ith row of X.

Using this notation, the predicted response for the ith row of X is given by:

Equation shown here

The variance of the prediction for ith row of X is given by:

Equation shown here

and the relative prediction variance is given by:

Equation shown here

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