clc
clear all
x=[-2 -1 0 1 2]
y=[15 1 1 3 19]
N=length(x)
M=[N sum(x); sum(x) sum(x.^2)]

L=inv(M)*B

f=L(1)+ L(2)*x
plot(x,y,'*r')
hold on
plot(x,f,'b-')

M1=[N sum(x) sum(x.^2); sum(x) sum(x.^2) sum(x.^3); sum(x.^2) sum(x.^3) sum(x.^4)]
B1=[sum(y);sum(x.*y);sum(x.^2.*y)]
L2=inv(M1)*B1
f1=L2(1)+L2(2)*x+L2(3)*x.^2
plot(x,f1,'k-')
***************************************************
x1=[-2 -1 0 1 2];
y1=[15 1 1 3 19];
syms x y a b 
n=length(x1);
g=@(a,b,x,y)((y-a-b*x))^2;
g1=@(a,b,x)(a+b*x);
h = diff(g,a);
h1 = diff(g,b);
k = subs(h, {x,y}, {x1,y1});
k1 = subs(h1, {x,y}, {x1,y1});
m = sum(k);
m1 = sum(k1);
equations = [m==0, m1==0]
[A c] = equationsToMatrix(equations);
X=inv(A)*c;
a1=X(1)
b1=X(2)
f=g1(a1,b1,x1);
plot(x1,y1,'r-*',x1,f,'b-^');








n= input("Enter the number of data points : ");
x= input("Data Points : ");
f= input("Value of f(x) : ");
A= zeros(2,2);
B= zeros(2,1);
A(1,1)=n;
for i=1:n
A(1,2)= A(1,2)+x(i);
A(2,2)= A(2,2) + (x(i)*x(i));
B(1)= B(1)+f(i);
B(2)= B(2) +(f(i)*x(i));
end
A(2,1)= A(1,2);
Solution= linsolve(A,B);
fprintf("Value of a : %0.5f\nValue of b :
%0.5f",Solution(1),Solution(2));