load population.dat
x=population;

N=length(x)
xn = x(1:N-1);
xnp1 = x(2:N);

figure(1)
plot(xn,xnp1,'*')

del = xnp1-xn;
figure(2)
plot(xn,del,'*')

delbyx = del./xn;

figure(3)
plot(xn,delbyx,'*')


A = sum(xn.^2);
B = sum(xn);
K = N-1;

MA = [A,B;B,K]
R = [sum(xn.*delbyx);sum(delbyx)]

ans = MA\R

y = ans(1)*xn+ans(2);
figure(4)
plot(xn,delbyx,'*',xn,y,'--')

figure(5)

plot(xn,xnp1,'*',xn,xn+xn.*y)

X = [0:10:700];
Y = X.*(ans(1)*X+ans(2));

figure(5)

plot(xn,xnp1,'*',X, X+Y)

figure(4)
plot(xn,delbyx,'*',X,(ans(1)*X+ans(2)),'--')