%Example 1 using the normal equation

x=[2 5 7 8]'; y=[1 2 3 3]';

numpts=length(x);  % This is how many data points we have

A=[x ones(numpts,1)]; % Build the matrix A

c=inv(A'*A)*A'*y;  % c is the least squares slope/intercept

fprintf('The slope is: %f, the intercept is: %f\n',c(1),c(2));
%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(0,8);   %Create test data
yTest=c(1)*xTest+c(2); %Create the line using the test data
plot(x,y,'k*',xTest,yTest,'k-');  % Plot the data with the line