clc
clear all

x = [0 0.5 1 1.5 2 2.5];
y = [0.4326 -0.1656 3.1253 4.7877 4.8535 8.6909];

n = 6;

xi = 0;
yi = 0;
xiyi = 0;
xisqr = 0;

for i = 1:n
    xi = xi + x(i);
    yi = yi + y(i);
    xiyi = xiyi + x(i) * y(i);
    xisqr = xisqr + (x(i))^2;
end

a = (n * xiyi - xi * yi) / (n * xisqr - xi^2);
b = (xisqr * yi - xi * xiyi) / ((n * xisqr) - (xi^2));

fx = a * x + b;

error = 0;
for i = 1:n
    error = error + (y(i) - (a * x(i) + b)) ^ 2;
end



plot(x, y, 'bo', x, fx, 'r-');
xlabel('x');
ylabel('y');
title('Linear Regression');
legend('Original Data', 'Fitted Line');

disp(['Sum of squared errors: ', num2str(error)]);