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From Wikipedia

a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows studying the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.

A "response variable" is the output in a prediction function (i.e. regression or classification), and "factors" are the components of the input of the prediction function.

So is it correct that factorial experiment is only used for collecting pairs of input and output of a prediction function in regression or classification.

Thanks!

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up vote 1 down vote accepted

A factorial experiment is not a classification framework for the response variable isn't a class, but yes you can make an analogy between regression and factorial design because generally speaking they are the same thing. The purpose of any supervised experiment is to collect the data you really need so you can put any study hipothesis to the test. Now, prediction in this case would be more like trying to interpolate for an untested combination of levels, you could do a regression with a dataset collected trough a factorial experiment and of course you can get some estimates this way, but being honest this is not the spirit of the technique.

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