fitRegressionLine.m

%============================================================================
% Copyright (C) 2014, Heikki Hyyti
%
% Permission is hereby granted, free of charge, to any person obtaining a
% copy of this software and associated documentation files (the "Software"),
% to deal in the Software without restriction, including without limitation
% the rights to use, copy, modify, merge, publish, distribute, sublicense,
% and/or sell copies of the Software, and to permit persons to whom the
% Software is furnished to do so, subject to the following conditions:
%
% The above copyright notice and this permission notice shall be included in
% all copies or substantial portions of the Software.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
% THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
% DEALINGS IN THE SOFTWARE.
%============================================================================

function [a,b] = fitRegressionLine(x, y)
    A11 = x' * x;
    A12 = sum(x);
    A21 = A12;
    A22 = size(x,1);

    B11 = y(:,1)' * x;
    B21 = sum(y(:,1));
    
    a = (A12*B21 - A22*B11) / (A12*A21 - A11*A22);
    b = (A11*B21 - A21*B11) / (A11*A22 - A12*A21);
end