MATLAB: How to plot prediction and confidence interval

confidence intervalCurve Fitting Toolboxlinear regressionprediction interval

Hi all,

I try to plot a prediction interval and a Confidence interval, of a linear regression fit. The prediction interval seem to be fine, but the confidence interval seems to be wrong. For the confidence interval I use ‘’ confint’’, see File.

Suggestions? Thanks a lot!!!

Matlab r2014a

Best Answer

p = predint(fitresult,x,0.95,'observation','off');
ci = confint(fitresult,0.95);
ciup = polyval( ci(2,:),x);
cilow = polyval(ci(1,:),x);

NO! ci ARE the confidence limits; they are bounds on the coefficients themselves, hence only an upper/lower for each of the N+1 coefficients. Remove the last two lines entirely; they're a total misuse of ci

All you can plot for them would be something like

   errorbar([0 1],coeffvalues(fitresult),ci(1,:),ci(2,:),'x')

Related Solutions

MATLAB: How to work with CFIT objects in curve fitting

You can use the function CONFINT to find confidence intervals. Full documentation on this function is available at

https://www.mathworks.com/help/curvefit/cfit.confint.html

Here is an example. Suppose that we have exported a fitted model from CFTOOL to the workspace.

fittedmodel1 =
     General model:
       fittedmodel1(x) = a*sin(x) + b
     Coefficients (with 95% confidence bounds):
       a =       1.018  (0.938, 1.097)
       b =    -0.03808  (-0.09455, 0.01839)

Now use CONFINT to get confidence intervals:

 confint(fittedmodel1)
ans =
    0.9380   -0.0946
    1.0973    0.0184

Here, the first column is the 95% confidence interval on the first parameter and the second column is the 95% confidence interval on the second parameter. A second input to CONFINT can give other levels of confidence.

To get the actual parameter values, use structure indexing. For example, parameter a could be found by typing

fittedmodel1.a

Another function of interest is PREDINT, to find prediction intervals. Full documentation for this function is available at

https://www.mathworks.com/help/curvefit/predint.html

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 work with CFIT objects in curve fitting

MATLAB: Estimate confidence intervals after regress!

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