Calculate out of sample linear fit predictions using pseudo-inverse. Please see: https://win-vector.com/2019/01/08/a-beautiful-2-by-2-matrix-identity/. Zero indexed.
xlin_pfits(x, y, w, i, j)
NumericVector, explanatory variable (length>=2).
NumericVector, values to fit.
NumericVector, weights (positive).
integer, first index (inclusive).
integer, j>=i+2 last index (inclusive);
vector of predictions.