MATLAB: Confidence interval for least square fitting

confidence intervalleast-square

Hi, i have a system of equations of the form Ax=b. with A and b known matrics, i calculates x using least square method. Now i want to calculate confidence interval on my estimated values in x. Any idea how should i proceed?

Best Answer

For the parameter confidence intervals in a linear problem, use the regress function. The ‘bint’ output will have them.

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MATLAB: Uncertainties and confidence intervals for both linear and nonlinear regression

I am not sure what do you mean by ‘the uncertainty of such parameters’?

The standard deviations of the estimated parameters are the square roots of the diagonals of the estimated variance-covariance matrix. In the nlinfit documentation, this is CovB.

The confidence interval (95% is the default) is the probability that the uncertainty of the parameter estimate includes zero. If it does (one of the confidence bounds is positive and the other negative), then that parameter is not needed in the regression model with the data you supplied to it. The confidence interval is therefore more meaningful than the variance or standard deviation.

MATLAB: Plot confidence interval of a signal

In order to calculate the 95% confidence intervals of your signal, you first will need to calculate the mean and *|std| (standard deviation) of your experiments at each value of your independent variable. The standard way to do this is to calculate the standard error of the mean at each value of your independent variable, multiply it by the calculated 95% values of the t-distribution (here), then add and subtract those values from the mean. The plot is then straightforward. (The tinv function is in the Statistics and Machine Learning Toolbox.)

Example —

x = 1:100;                                          % Create Independent Variable
y = randn(50,100);                                  % Create Dependent Variable ‘Experiments’ Data
N = size(y,1);                                      % Number of ‘Experiments’ In Data Set
yMean = mean(y);                                    % Mean Of All Experiments At Each Value Of ‘x’
ySEM = std(y)/sqrt(N);                              % Compute ‘Standard Error Of The Mean’ Of All Experiments At Each Value Of ‘x’
CI95 = tinv([0.025 0.975], N-1);                    % Calculate 95% Probability Intervals Of t-Distribution
yCI95 = bsxfun(@times, ySEM, CI95(:));              % Calculate 95% Confidence Intervals Of All Experiments At Each Value Of ‘x’
figure
plot(x, yMean)                                      % Plot Mean Of All Experiments
hold on
plot(x, yCI95+yMean)                                % Plot 95% Confidence Intervals Of All Experiments
hold off
grid

This should get you started.

Best Answer

Related Solutions

MATLAB: Uncertainties and confidence intervals for both linear and nonlinear regression

MATLAB: Plot confidence interval of a signal

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