function P3_05B2
clear, clc, format short g, format compact
xyData=[277	49000	2.3	0.947
348	68600	2.28	0.954
421	84800	2.27	0.959
223	34200	2.32	0.943
177	22900	2.36	0.936
114.8	1321	246	0.592
95.9	931	247	0.583
68.3	518	251	0.579
49.1	346	273	0.29
56	122.9	1518	0.294
39.9	54	1590	0.279
47	84.6	1521	0.267
94.2	1249	107.4	0.724
99.9	1021	186	0.612
83.1	465	414	0.512
35.9	54.8	1302	0.273];
X=xyData(:,2:end);
m=size(X,1); %Determine the number of data points
Y=xyData(:,1);
prob_title = ([' Heat Transfer Correlation - Noninear Regression 2']);
dep_var_name=['Nu '];
ind_var_name=['RE'];
parm=[0.5347 0.5588 0.2524 -0.06772];
npar=size(parm,2); % Determine the number of the parameters
options=optimset('MaxFunEvals',1000); % Change the default value for MaxFunEvals
Beta=fminsearch(@NonlinFun,parm,options,X,Y); % Find optimal parameters using fminsearch
[f,Ycalc]=NonlinFun(Beta,X,Y); % Compute Y (calculated) at the optimum
disp(['   Results,' prob_title ]); 
Res=[];
for i=1:npar
	Res=[Res; i Beta(i)];
end
disp('     Parameter No.   Value      ');
disp(Res);
sigmar=0;
Var=0;
for i=1:m
    Var=Var+ ((Ycalc(i)-Y(i)))^2;
    sigmar=sigmar+((Ycalc(i)-Y(i))/Y(i))^2;
end
disp(['  Variance ', num2str(Var/(m-npar))]);
disp([' Relative variance ', num2str(sigmar/(m-npar))]);  
plot(Y,Y-Ycalc,'*')	% Residual plot			
title(['Residual Plot, ' prob_title ])				
xlabel([dep_var_name '(Measured)'])				
ylabel('Residual')				
function [f,Ycalc]=NonlinFun(parm,X,Y)
a=parm(1);
b=parm(2);
c=parm(3);
d=parm(4);
for i=1:size(X,1);
Ycalc(i,1)=a*X(i,1)^b*X(i,2)^c*X(i,3)^d;
end
resid(:,1)=Y-Ycalc;
f=resid'*resid;