% Get Data
t = [1 3 5 7 9]';
y = [0.076 0.258 0.369 0.492 0.559]';

% Function to Fit
phi='GNexpfunc';

% Initial Guess for beta
beta_0 = ones(2,1);

% First run the optimzation routine
[beta,res,J,Cov_beta,mse] = nlinfit(t,y,phi,beta_0);

SE=sqrt(diag(Cov_beta));

%y_beta = feval(phi,beta,tvec);
dt=mean(diff(t));
tvals=linspace((t(1)-dt),(t(end)+dt),1000);
[y_beta delta]=nlpredci(phi,tvals,beta,res,'jacobian',J);

ci = nlparci(beta,res,'jacobian',J);

figure(1)
clf
plot(t,y,'r*',tvals,y_beta)
hold on
title('Data and non-linear least squares fit')
plot(tvals,y_beta+delta','g')
plot(tvals,y_beta-delta','g')
legend('data','model','95% prediction interval','location','best')

fprintf('\nEstimates:\n')
fprintf('\tbeta_0=%f\t\tSE=%f\t\t95percent CI:  [%f,%f]\n',beta(1),SE(1),ci(1,1),ci(1,2))
fprintf('\tbeta_1=%f\t\tSE=%f\t\t95percent CI:  [%f,%f]\n',beta(2),SE(2),ci(2,1),ci(2,2))

fprintf('Non-linear fit is %f - exp(-%f*t)\n\n',beta(1),beta(2))

beta