% mm3804.m
% find weighted polynomial coefficients using lscov
x=[0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1]';
y=[-.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.48 9.30 11.2]';
n=3;
pm=polyfit(x,y,n);
m=length(x);  % number of elements in x
V=ones(m,n+1); % preallocate memory for result
for i=n:-1:1  %build V column by column
   V(:,i)=x.*V(:,i+1);
end
w=ones(size(x));
w(4)=2^2;
w(7)=10^2;
p=lscov(V,y,w)';
xi=linspace(0,1,100);
ym=polyval(pm,xi);
yw=polyval(p,xi);
pt=false(size(x));
pt([4 7])=true;
plot(x(~pt), y(~pt),'x', x(pt) ,y(pt) ,'o', xi,ym, '--',xi,yw)
xlabel('x'),ylabel('y=f(x)')
title('Figure 38.4:Weighted Curve Fitting')