# Confirmation¶

Confirmation is intended to be used to confirm that the model can predict actual outcomes at the optimal settings determined from the analysis.

Additional confirmation runs ($$n_c$$) are conducted at the optimal settings. The average of those runs is compared to the prediction interval for a sample of size $$n_c$$. The larger the $$n_c$$, the smaller the interval. Smaller intervals indicate good precision in the estimates.

The L% PI (prediction interval) L% of prediction intervals generated from similar experiments will contain the average of a future sample. If the sample size is one, then it can be thought of as the next observation.

The default value for L is 95% = (1-0.05)*100%; this value can be changed on the Edit, Preferences – General, Analysis node.

A prediction interval will be larger (a wider spread) than the confidence interval because there is more scatter expected from a small sample estimating the average versus the entire population’s true mean.

Stat-Ease does not recommend extrapolating outside of the design space due to the increased prediction error. No data has been gathered beyond the region of the experiment.

The program does allow for extrapolation of numeric factors (categorical factors and mixture components cannot be extended beyond their tested ranges.) Use the Sheet view on the Factors tool palette and enter the desired extrapolated factor levels. Factor levels outside of the design space will generate a warning message along with the predicted results. This feature is useful for exploration of a potential expanded design space.

Math details:

$$L\%\,Prediction\,Interval=\widehat{\overline{y}}_{0}\,\pm t_{(1-\frac{\alpha}{2},\, residual\, df)}\cdot SE_{pred}$$

$$SE_{pred}=s\sqrt{\frac{1}{n_c}+x_{0}(X^T\, X)^{-1}\,x_{0}^{T}}$$