%Class for CO907.
%__________________________________________
%Author: Jiarui Cao
%Date: 19 Nov 2013
%Purpose: Problem Sheet 2. Q2.5b


close all;
clear all;
clc;
clf;

n=200;
rng('default');
%% generate data
y=normrnd(0,1/2,n,1);

for i=1:n
x(i)=sin(2*pi*i/n)+y(i);
%x(i)=1+(i/n)^2;
t(i)=i/n;
end


hold on
plot(t,x,'or');

%% polynomial least squares estimate. 
%%M=4
p=polyfit(t,x,4);
yfit = polyval(p,t);
plot(t,yfit,'k');

%%M=3
p=polyfit(t,x,3);
yfit = polyval(p,t);
plot(t,yfit,'--b');

legend('Data','M=4','M=3');

xlabel('t');
ylabel('X_t');