How Many Predictors Are Needed?
q Very often, one predictor is a function of the other predictors.
q It becomes an important question: How many predictors do we
need in order to make a good regression (or prediction)?
q Does increasing the number of the predictor improve the
regression (or prediction)?
q If too many predictors are used, some large coefficients may be
assigned to variables that are not really highly correlated to the
predictant (y). These coefficients are generated to help the
regression relation to fit y.
q To answer this question, we have to figure out how fast (or slow)
the “fraction of explained variance” increase with additional
number of predictors.