Given that you have created one or more models the final thing to do is interpret them to see what they’re telling you. There are two main activities here:

Exploring the model parameters can be done in a variety of ways: you can look at the numbers to see how big or small they are, as well as which direction they point (positive or negative). This is usually informative up to a point, particularly for main effects, but can get harder to interpret where interactions are concerned.

Typically what you’re looking for here is to see which ones are near zero and which ones seem to have a large effect. Beware that in many packages (including Synthace) the model terms are scaled by the size of the change in the data so if your range is +/- 10 the same coefficient would be much bigger than it would be if the range were +/- 1000 but it had the same effect on the response.

Another useful tool for exploring coefficients is the graphical profiler. This allows you to use sliders to change the values of parameters and see both the effect on the response but most importantly how the effects of the other factors change. This is a very good way to see how interactions work: a strong interaction will lead to the slope of another factor changing, while where there’s no interaction the line will just move up or down without changing slope.

Making predictions from single models can be done automatically for you by the software once you have told it whether you want to maximize or minimize the response.

For models with only main effects and interactions these predictions will always be at one or other of the corners of the design space, and may not be terribly interesting - you could guess where the optimum will be by looking at the slopes, although it would be a bit tedious to do so.

For models with quadratic effects the predictions get more interesting since these models can be curved in the middle, leading to optima that could be anywhere in the space.

It’s very common to have more than one response of importance: for example you may be producing something and need it both to be made in large amounts and with a low level of byproducts.

In this situation you can often enter a situation where these two goals would lead you in slightly different directions - leading to a need to trade off between them.

This can also be handled automatically by first building models in each of the different responses separately, then jointly optimizing all the responses at once. Sometimes this will give you a fairly clear result but often you may need to explore a range of possibilities and find one that’s good enough in all ways rather than being optimal in any one. Graphical tools are usually used for this purpose, and typically you would try to constrain one response to be higher than a given threshold then exploring what values of the other are possible given that constraint.

To learn more about the statistics behind model prediction, click here.

To learn how to predict the best conditions from your model in Synthace, click here.

To learn how to predict the best conditions from multiple models in Synthace, click here.