function leastsquare(filename,n)
%%input the filename 'data.dat', and 
%%the degree of polynomial n

data=load(filename);

%data m X 2 size
[m,l]=size(data);
m

%The matrix A is a (n+1)X(n+1) matrix.
%b is the right hand side (n+1)X(1) vector
A=zeros(n+1);
b=zeros(n+1,1);

for i=1:n+1
    for j=1:n+1
        for k=1:m
            A(i,j)=A(i,j)+data(k,1)^(i+j-2); %(i,j)element of A
        end
    end
end


for i=1:n+1
    for k=1:m
        b(i)=b(i)+(data(k,1)^(i-1))*data(k,2); %ith element of b
    end
end

%find the solution
y=inv(A)*b;


%define the domain to plot the solution
a=min(data(:,1));
b=max(data(:,1));

%divide the domain into 100 small subinterval,
%so we are going to evaluate the polynomial 
%at 101 evenly spaced points in the domain.
z=zeros(101,1);
for i=1:101
    for j=1:n+1
        z(i)=z(i)+y(j)*(a+(b-a)*(i-1)/100)^(j-1);
    end
end

x=a:(b-a)/100:b;

plot(x',z,'red');
hold on;
plot(data(:,1),data(:,2));
hold off;