//Example 6.9
//Least Square Fit
//Page no. 224
clc;close;clear;

x=[-3,-1,1,3]
y=[15,5,1,5]
n=1;
printf('\t\t 2\t 3\t 4\t\t\t 2\n n\tx\tx\tx\tx\ty\txy\tx y\n----------------------------------------------------------------\n')
x1=0;x2=0;x3=0;x4=0;x5=0;x6=0;x7=0;x8=0;
for i=1:4
    printf(' %g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\n',n,x(i),x(i)^2,x(i)^3,x(i)^4,y(i),y(i)*x(i),x(i)^2*y(i))
    x1=x1+n;
    x2=x2+x(i);
    x3=x3+x(i)^2;
    x4=x4+x(i)^3;
    x5=x5+x(i)^4;
    x6=x6+y(i);
    x7=x7+y(i)*x(i);
    x8=x8+x(i)^2*y(i)
end
printf('----------------------------------------------------------------\n %g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\n',x1,x2,x3,x4,x5,x6,x7,x8)
A=[x1,x2,x3;x2,x3,x4;x3,x4,x5]
B=[x6;x7;x8]
C=inv(A)*B;
disp(C)
x=poly(0,'x')
y=C(1)+C(2)*x+C(3)*x^2
disp(y,'y =')