function [betaHat, aHat] = olsEstimates(X, y);
% olsEstimates Estimates parameters for OLS.
%
% Parameters for a multiple regression are estimated by using OLS.
% All variables (dependent and independent) are standardized
% and estimates for standardized and original units are calculated.
%
% USE:
% [betaHat, aHat] = olsEstimates(X, y)
%
% betaHat = Estimates in standardized unit,
% aHat = Estimtes in the original unit.
%
% X = independent variable (include a column of ones for intercept)
% y = dependent variable.  

% Tomo Eguchi
% 28 January 2002

%X1 = normrnd(4,3,30,1); X2=normrnd(5,20,30,1);X3=normrnd(12,3,30,1);X4=normrnd(0,3,30,1);
%X = [ones(30, 1), X1, X2, X3, X4];
%X1 = [ones(30, 1), X];
%trueA = [4; 3; 12; 9; 5];
%y = X*trueA + normrnd(0, 1, 30, 1);

[sampleSz, nPars] = size(X);          % find the dimension of data matrix
Int = 0;                              % initialize the intercept term
if (sum(X(:, 1)) == sampleSz),        % if the first column of the data matrix
   X = X(:, 2:end);                   % sums to the sample size, then there is an
   Int = 1;                           % intercept term.
end
   
corX = cor(X);                        % compute correlation matrix of X
corXy = cor(X, y);                    % compute correlation vector between X and y

betaHat = inv(corX) * corXy';         % estimate parameters in standardized unit

sdY = std(y);                         % compute standard deviations of X and y
sdX = std(X);

aHat = ((sdY./sdX) .* betaHat')';        % compute back into the original unit.
if Int == 1,                          % if there is an intercept, compute that too.
   a0 = mean(y) - mean(X) * aHat;
   aHat = [a0; aHat];
end