# 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.