LSappx.m

clear;

%% Data Set
t = [-2; -1;  0;  1;  2];
y = [ 4;  3;  1; -1; -3];

%% Degree of approximation
% n = 1; % linear
% n = 2; % quadratic
% n = 3; % cubic
n = 4; % quartic

%% Prepare A
A = zeros(size(t, 1), n+1);
for i = 1:1:n+1
    A(:, i) = t .^ (n - i + 1);
end

%% Solve x & Compute Error
x = ((A' * A) \ A') * y;
e = sum((A * x - y) .^ 2);

%% Compute exact values
tapp = linspace(min(t)-1, max(t)+1);
yapp = ones(size(tapp)) .* x(end);
for i = 1:1:n
    yapp = yapp + (tapp .^ (n - i + 1)) .* x(i);
end

%% Plot
hold on;
grid on;
plot(t, y, 'o');
plot(tapp, yapp);
xlabel('t'); ylabel('y');
title(['Error ~= ', num2str(e)]);
legend('origin data set', ['approx. n = ', num2str(n)]);
hold off;