% -*- texinfo -*-
% @deftypefn {Function File} {[@var{b}, @var{bint}, @var{r}, @var{rint}, @var{stats}] =} regress (@var{y}, @var{X}, [@var{alpha}])
% Multiple Linear Regression using Least Squares Fit of @var{y} on @var{X}
% with the model @code{y = X * beta + e}.
%
% Here,
%
% @itemize
% @item
% @code{y} is a column vector of observed values
% @item
% @code{X} is a matrix of regressors, with the first column filled with
% the constant value 1
% @item
% @code{beta} is a column vector of regression parameters
% @item
% @code{e} is a column vector of random errors
% @end itemize
%
% Arguments are
%
% @itemize
% @item
% @var{y} is the @code{y} in the model
% @item
% @var{X} is the @code{X} in the model
% @item
% @var{alpha} is the significance level used to calculate the confidence
% intervals @var{bint} and @var{rint} (see `Return values' below). If not
% specified, ALPHA defaults to 0.05
% @end itemize
%
% Return values are
%
% @itemize
% @item
% @var{b} is the @code{beta} in the model
% @item
% @var{bint} is the confidence interval for @var{b}
% @item
% @var{r} is a column vector of residuals
% @item
% @var{rint} is the confidence interval for @var{r}
% @item
% @var{stats} is a row vector containing:
%
% @itemize
% @item The R^2 statistic
% @item The F statistic
% @item The p value for the full model
% @item The estimated error variance
% @end itemize
% @end itemize
%
% @var{r} and @var{rint} can be passed to @code{rcoplot} to visualize
% the residual intervals and identify outliers.
%
% NaN values in @var{y} and @var{X} are removed before calculation begins.
%
% @end deftypefn