# terminology for 'raw' vs 'derived' predictor variables

Many regression-like statistical methods use the general approach of mapping from a set of 'raw', actually observed variables to a larger set of variables that are the actual space of inputs to the regression, via (for example)

• basis expansion ([orthogonal] polynomial, spline, etc.)
• conversion of categorical variables to dummy variables according to some contrast scheme

For example, if I started with a Wilkinson-Rogers/R formula ~ poly(x,2) + f (where x is numeric and f is a factor/categorical variable),

1. x and f would be my [???] variables
2. (Intercept), poly(x, 2)1, poly(x, 2)2, fB (the columns of my model matrix) would be my [???] variables

I have a vague memory that I've used "input" for #1 and "predictor" for #2 in the past, but I don't know where I got that from or whether I've gotten it reversed from the original source. Can anyone point me to clear/useful/established terminology that distinguishes between these two types of (covariates/features/(independent|explanatory|predictor) variables) ?

(Slightly related to Regression terminology, predictor vs IV vs?)

We refer to the $$X$$-variables in the regression as predictors or "predictor variables" ... we use the term inputs for the information on the units that goes into the $$X$$-variables. Inputs are not the same as predictors. For example, consider the model that includes the interaction of maternal education and maternal IQ:
$$\textrm{kid.score} = 58 + 16 \cdot \textrm{mom.hs} + 0.5 \cdot \textrm{mom.iq} - 0.2 \cdot \textrm{mom.hs} \cdot \textrm{mom.iq} + \textrm{error}$$