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.