function P3_05B1
clear, clc, format short g, format compact
xyData=[277	49000	2.3
348	68600	2.28
421	84800	2.27
223	34200	2.32
177	22900	2.36
114.8	1321	246
95.9	931	247
68.3	518	251
49.1	346	273
56	122.9	1518
39.9	54	1590
47	84.6	1521
94.2	1249	107.4
99.9	1021	186
83.1	465	414
35.9	54.8	1302];
X=xyData(:,2:end);
m=size(X,1); %Determine the number of data points
Y=xyData(:,1);
prob_title = ([' Heat Transfer Correlation - Noninear Regression 1']);
dep_var_name=['Nu '];
ind_var_name=['RE'];
parm=[0.6623 0.5395 0.2454];
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);
for i=1:size(X,1);
Ycalc(i,1)=a*X(i,1)^b*X(i,2)^c;
end
resid(:,1)=Y-Ycalc;
f=resid'*resid;