%ex1

%define variables
syms a b c
%define data
x=[1,2,3,4];
y=[7,6,4,1];
%define your function
f=0;
for i=1:length(x)
f=f+((a*x(i)^2+b*x(i) +c)-y(i))^2;
end
%calculate derivatives
da=diff(f,a);
db=diff(f,b);
dc=diff(f,c);
%solve the equations
sol=solve([da==0,db==0,dc==0],[a,b,c]);
%plot the solution
x1=0:0.1:5;
y1=sol.a*x1.^2+sol.b*x1+sol.c
figure(1)
plot(x1,y1,'r');
hold all;
for k=1:length(x);
figure(1)
plot(x(k),y(k),'bo');
end
hold off; grid on;
xlabel('X'), ylabel('Y'),
title('Linear approximation')