% Example 3, Section 6.5

%Make up some noisy data.
x=3*pi*rand(40,1);  %40 random numbers between 0 and 3*pi
x=sort(x);
y=-sin(x)+3*sin(2*x)-0.5*cos(x)+4*cos(3*x)+randn(size(x));

%Create matrix A:
A=[sin(x) sin(2*x) cos(x) cos(3*x)];
c=inv(A'*A)*A'*y

%Computing the error between y and the values on the line:
Err=norm(y-A*c);
fprintf('The error is: %f\n',Err);

xTest=linspace(0,10)';   %Create test data
yTest=[sin(xTest) sin(2*xTest) cos(xTest) cos(3*xTest) ]*c;
plot(x,y,'k*',xTest,yTest,'k-');