| Synopsis
| Least Squares approximation removing the least significant variable.
LSBestDelete finds the least significant independent variable to remove.
This variable is least significant in the sense that increases the norm
of the residuals by the least amount. This is the reverse process of
Stepwise regression, where we start with all the independent variables
and remove the one with the least norm increase at a time.
Problem: Given a matrix of A (dim n x m) and a vector b (dim n), we want
to find a vector x (dim m) such that Ax ~ b, where x has one entry
which is zero. This approximation is in the least squares sense,
i.e. ||Ax-b||^2 is minimum.
The calling arguments are:
AtA is a matrix (dim m x m) which is the product A^t * A
btA is a vector (dim m) which is the product b^t * A
btb is the norm squared of b, i.e. b^t * b
Output: The output is a list with two values: [i,norm], where
i is the index of the variable removed
norm is the value of the norm of the residuals without this variable
i.e. norm = ||Ax-b||^2
See Also: ?LSBestSum ?LSBestSumDelete |