fstats_doe_prediction Module

DOE predictions with confidence and prediction intervals.

This module evaluates a doe_model at a set of factor values and returns the predicted responses along with confidence and prediction intervals. With $\mathbf{x}_{0}$ the design-matrix row (model terms) for a prediction point, $C = \left( X^{T} X \right)^{-1}$ the unscaled parameter covariance of the fit, $MSE$ the residual mean squared error, and $t$ the critical value of Student's t distribution with $\nu = m - p$ degrees of freedom at probability $1 - \alpha / 2$, the intervals are

$$\hat{y} \pm t \sqrt{MSE \cdot \mathbf{x}_{0}^{T} C \mathbf{x}_{0}}$$ $$\hat{y} \pm t \sqrt{MSE \left( 1 + \mathbf{x}_{0}^{T} C \mathbf{x}_{0} \right)}$$

for the mean response (confidence interval) and for a new observation (prediction interval), respectively. The factor values must be in the same scale (e.g. coded on [-1, 1]) used when the model was fit.

The covariance matrix and the residual statistics are stored in the model by doe_fit_model. For a model that was not created by doe_fit_model, supply the factor values used to fit the model (x_fit) and the residual mean squared error (residual_mse) to the routines.