 # Interpreting Models¶

Models are used to produce graphs, optimization and post analysis output. The graphs are easier to interpret than looking at the models directly. The following is a quick guide for how to interpret models.

## Numeric Factors¶

A factorial model is composed of a list of coefficients multiplied by their associated factor levels.

The models include an intercept, main effects for the single factor effects, and interactions where the effect of one factor depends on the settings of the other factors in the interaction. Curvature is a term that can be estimated if center point runs are included.

$$\widehat{\overline{Y}}=\beta_{0}+\beta_{1}A+\beta_{2}B+\beta_{3}C+\beta_{12}AB+\beta_{13}AC+\beta_{23}BC+...+Curvature$$

The beta (β) coefficients in the above model are the slope indicating how much change is expected in the response (Y) when there is a one unit change in the factor (A, B, C, …). When there are two or more factors in a term then it is easiest to interpret the model by setting all but one to a fixed value. Multiply the coefficient times the fixed factor settings to get a provisional coefficient for the remaining, variable factor.

## Categoric Factors¶

When a categoric factor has two levels, it interprets the same as a numeric factor. When a categoric factor has more than two levels, interpretation becomes a bit more difficult. Please see the Hints and FAQ topic on Interpreting the Categoric Model

## Mixture Components¶

Mixture models are only readily interpretable when the mixture components all go from 0 to the total for the design. Most mixtures designs cover a more constrained space. Use the Model Graphs to better understand the models.

See the Scheffé Mix Model topic in Mixture Designs for more details.