Linear Least Squares Regression Analysis by a MATLAB program

A MATLAB program is developed to determine the coefficients by linear least squares regression where the function is, y = mx + b. Here,

x	-6	-4	-1	0	3	5	8
y	18	13	6	4	-1	-8	-15

% A function defined for least square regression

function [c,R2] = linearregression(x,y)

% Least-squares fit of data to y = c(1)*x + c(2)

% Here, c(1) = m; c(2) = b;

% Inputs:

% x,y = Vectors of independent and dependent variables

% Outputs:

% c = Coefficients of the given equation

if length(y)~= length(x)

    error("x and y are not compatible");

end

% Least squares algorithm implementation

x = x(:); y = y(:); % x and y are column vectors

A = [x ones(size(x))]; % m-by-n matrix of the system

c = (A'*A)\(A'*y); % Solving normal equations

if nargout>1 % Checking number of function outputs

r = y - A*c;

R2 = 1 - (norm(r)/norm(y-mean(y)))^2;

end

Program Output:

>> x = [-6 -4 -1 0 3 5 8];

>> y = [18 13 6 4 -1 -8 -15];

>> linearregression(x,y)

ans =

   -2.3140

    4.0814