As you may have noticed already, the data have a huge variance around that fit:
x = [6 10 14 20 26 34 38]';
y = [122 107 119 120 105 95 92]';
% Tabulate the data
tbl = table(x,y);
% % Fit the model
% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x) F(1).*exp(-x/F(2));
beta0 = [1 1];
mdl = fitnlm(tbl,f,beta0)
% Calculate the model values at the empirical x
y_predicted = predict(mdl,x);
% Plot the data and fit
figure
plot(x,y,'*',x,y_predicted,'g');
legend('data','fit')
But, here is the code to build the bootstrap intervals. b in particular has a huge variance, and the fit to the resampled data off throws off warnings. I turned off warnings here, so you don't have to scroll through all of them to see the output, but I recommend leaving them on locally, so that you can investigate them. Caveat emptor.
rng default
x = [6 10 14 20 26 34 38]';
y = [122 107 119 120 105 95 92]';
numberObservations = numel(x);
NUMBER_RESAMPLE = 5000;
bootstrappedCoefficients = zeros(2,NUMBER_RESAMPLE);
warning("off")
for nr = 1:NUMBER_RESAMPLE
% if mod(nr,100)==0
% fprintf("Iteration %d of %d",nr,NUMBER_RESAMPLE)
% end
resampleIdx = randsample(numberObservations,numberObservations,true);
xr = x(resampleIdx);
yr = y(resampleIdx);
% Tabulate the data
tbl = table(xr,yr);
% % Fit the model
% Define function that will be used to fit data
% (F is a vector of fitting parameters)
f = @(F,x) F(1).*exp(-x/F(2));
beta0 = [1 1];
mdl = fitnlm(tbl,f,beta0);
bootstrappedCoefficients(:,nr) = mdl.Coefficients.Estimate;
end
warning("on")
figure
tiledlayout(2,1)
nexttile
histogram(bootstrappedCoefficients(1,:))
nexttile
histogram(bootstrappedCoefficients(2,:))
coef1 = median(bootstrappedCoefficients(1,:))
coef1_lo95 = prctile(bootstrappedCoefficients(1,:), 2.5)
coef1_hi95 = prctile(bootstrappedCoefficients(1,:), 97.5)
coef2 = median(bootstrappedCoefficients(2,:))
coef2_lo95 = prctile(bootstrappedCoefficients(2,:), 2.5)
coef2_hi95 = prctile(bootstrappedCoefficients(2,:), 97.5)
