First, there is the curse of dimensionality. As the number of predictors increases, the space the data needs to populate increases as a power...

First, there is the curse of dimensionality. As the number of predictors increases, the space the data needs to populate increases as a power function. Consequently, the demand for data increases very rapidly, and one risks the data that are far too sparse to produce a meaningful t. Second, there are often dicult conceptual problems associated with multiple predictors. For example, how is the neighborhood near x0 to be dened when predictors are correlated? Perhaps highly correlated predictors should be made less important when the distance to x0 is calculated. Or, should the units of the predictors be standardized? If not, predictors with more variability can dominate how the neighborhood is determined. Third, gaining meaningful access to the results is no longer straightforward. When there is more than two predictors, one can no longer graph the tted surface in the usual way. How then does one make sense of a surface in more than three dimensions?