MATLAB: Confidence intervals with lsqlin

confidenceintervallsqlinStatistics and Machine Learning Toolbox

Hi all,

I'd like to know if a function exists that computes the intervals of confidence of the result of the lsqlin optimisation given the intervals of confidence of the input data.

Using the notations here (<http://www.mathworks.fr/fr/help/optim/ug/lsqlin.html)>, I'm basically looking for confidence intervals of x components given the confidence intervals of d components.

Thanks in advance for your advice!

Best Answer

If you have constraints (looks like you do since you use lsqlin) then you will have to explore bootstrapping methods to estimate confidence intervals in the presence of constraints.

http://www.mathworks.com/help/stats/bootci.html

If you simply have bound constraints then you can transform your data as explained here:

http://www.mathworks.com/matlabcentral/answers/102066-how-do-i-find-the-confidence-intervals-for-the-estimated-coefficients-of-a-bounded-nonlinear-regress

If you do not have constraints or bounds, simply use fitlm which give you all the information you may need to assess your fit:

http://www.mathworks.com/help/stats/fitlm.html

Related Solutions

MATLAB: How to find the erro for fitted parameters

To get parameter confidence limits on a nonlinear regression, use the nlparci (link) function.

To get confidence intervals on the fit (prediction), use the nlpredci (link) function.

MATLAB: Estimate confidence intervals after regress!

The ‘BINT’ matrix contains the parameter confidence intervals.

If you want both parameter and prediction confidence intervals, use fitlm:

x = (1:10)';                                        % Create Data

y = 1.5 + 2.3*x + 1.5*randn(size(x));               % Create Data
mdl = fitlm(x, y);                                  % Fit Data
B = mdl.Coefficients.Estimate;                      % Coefficients
CI = coefCI(mdl);                                   % Coefficient Confidence Intervals
[Ypred,YCI] = predict(mdl, x);                      % Fitted Regression Line & Confidence Intervals
figure(1)
plot(x, y, 'pg')
hold on
plot(x, Ypred,'-r',    x, YCI, '--r')
hold off
grid

Best Answer

Related Solutions

MATLAB: How to find the erro for fitted parameters

MATLAB: Estimate confidence intervals after regress!

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