function P3_08BC
clear, clc, format short g, format compact
x1=[0.0464	0.0861	0.2004	0.2792	0.3842	0.4857	0.5824	0.6904	0.7842	0.8972]';
gamma1=[1.2968	1.2798	1.2358	1.1988	1.1598	1.1196	1.0838	1.0538	1.0311	1.0078]';
gamma2=[0.9985	0.9998	1.0068	1.0159	1.0359	1.0676	1.1096	1.1664	1.2401	1.4038]';
%xyData=[];
X=x1;
m=size(X,1); %Determine the number of data points
Y=gamma1+gamma2;
prob_title = (['Nonlinear Regression for Parameters of Margules Equations']);
dep_var_name=['gsum '];
ind_var_name=['x1'];
parm=[0.25 0.46];
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);
s2=sum((Y-Ycalc)'*(Y-Ycalc))/(m-npar); %variance 
disp(['  Variance ', num2str(s2)]);	
ymean=mean(Y);
R2=(Ycalc-ymean)'*(Ycalc-ymean)/((Y-ymean)'*(Y-ymean));%linear correlation coefficient
disp(['  Correlation Coefficient ', num2str(R2)])	
errsum=0;
for i=1:m
    gamma1c(i)= exp((1-x1(i)) ^ 2 * (2 * Beta(2) - Beta(1)) + 2 * (1-x1(i)) ^ 3 * (Beta(1) - Beta(2)));
     gamma2c(i)= exp(x1(i) ^ 2 * (2 * Beta(1) - Beta(2)) + 2 * x1(i)^ 3 * (Beta(2) - Beta(1)));
     errsum=errsum +(gamma1(i)-gamma1c(i))^2+(gamma2(i)-gamma2c(i))^2;
end
disp(['  Sum of squares of errors ', num2str(errsum)]);
plot(Y,Y-Ycalc,'*')	% Residual plot			
title(['Residual Plot, ' prob_title ])				
xlabel([dep_var_name '(Measured)'])				
ylabel('Residual')				
pause
plot(X,Ycalc,'r-',X,Y,'b+' ) %Plot of experimental and calculated data						
title(['Calculated/Experimental Data ' prob_title])						
xlabel([ind_var_name])						
ylabel([dep_var_name])
function [f,Ycalc]=NonlinFun(parm,X,Y)
A=parm(1);
B=parm(2);
for i=1:size(X,1);
    Ycalc(i,1)=exp((1-X(i))^2*(2*B-A)+2*(1-X(i))^3*(A-B))+exp(X(i)^2*(2*A-B)+2*X(i)^3*(B-A));
end
resid(:,1)=Y-Ycalc;
f=resid'*resid;