%plot1b.m Script for Linear Least Squares Fit with Plots and 
%  Goodness of Fit Paramters  -- J.M. Lockhart
%The data file must contain three columns: x-values, y-values, and
%  uncertainties in y-values. Uncertainties must be non-zero. 
datafile=input('Input the data file name ','s');
data=load( datafile)
x=data(:,1);
y=data(:,2);
e=data(:,3);
errorbar(x,y,e,e,'*');
hold
dim = size(x);
n=dim(1,1);
k=dim(1,2);
x=[ ones(n,1) x] ;
w = 1./e;
wsq=w.*w
%w=diag(w);
xtxi = inv(x'*x);
coef = xtxi*x'*y;
fits=x*coef;
my=sum(y)/n;
tl=fits'-ones(1,n)*my;
tll=tl*tl';
bl=y-ones(n,1)*my;
bll=bl'*bl;
rsq=tll/bll;
res=y-fits;
serr=(res'*res/(n-k-1))^.5;
c=serr^2*inv(x'*x);
c=sqrt(diag(c,0));
ttab=[coef,c,coef./c];
fval=(tll/k)*(n-k-1)/(bll-tll);
sigw=1./e
res=res.*sigw
rch=(res'*res/(n-k-1));
plot(x(:,2),fits)
slstr=num2str(coef(2));
intstr=num2str(coef(1));
lstr=[slstr,'x+',intstr];
ccst=['cc= ',num2str(sqrt(rsq))];
rchst=['rcs= ',num2str(rch)];
delmst=['delm= ',num2str(c(2))];
delbst=['delb= ',num2str(c(1))];
lstrm=str2mat(lstr,delmst,delbst);
lstrm2=str2mat(ccst,rchst);
legend(lstrm,lstrm2,0);