allregress(y,X,crit​eria)

All possible regressions of y on X, selecting the best model by a means of selection criteria

% This function runs all possible regressions of y on X, and selects the best model by a means of selection criteria
%
% Inputs:
% y - dependent variable, column vector, n-by-1
% X - explanatory variable matrix, consisting of k columns, n-by-k
% criteria - model selection criteria, choose between 'AIC', 'BIC'(default), 'R2', 'MSE'
%
% Outputs:
% M - Statistics of the selected model
% Iset - indices of the selected explanatory variables, a logic row vector, 1-by-k
%
% Example:
% y = randn(100,1);
% X = randn(100,6);
% [M_BIC, I_BIC] = allregress(y,X);
% [M_MSE, I_MSE] = allregress(y,X,'MSE');
%
% Author: Shen Liu, Queensland University of Technology, Australia
% Date: 2 March 2015