Plot Confidence Interval of 95%

Hi, I used the optimoptions to find the fitted curve of my result points, and now I'm trying to plot the points, the fitted curve and the confidence interval.

These are the points:

T0 = [-49;-45;-19;-20;30;30;100;98;238;239;350;349];

Y = [0;0;0;0;12;8;48;44;46;34;34;40];

And this is the code to find the fitted curve:

lb = [];

ub = [];

% Starting point

x0 = [10;10;10;10];

F = @(x) (x(1) + x(2)*tanh((x(3) - T0)/x(4)) );

Fobj = @(x,T0) F(x);

options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');

x = lsqcurvefit(Fobj,x0,T0,Y,lb,ub,options);

So how can I plot the points, the fitted curve and the confidence interval together?

Answer 1

[Star Strider]

The nlpredci funciton will work here, however in the presence of a constrained optimisation, no confidence limits may be reliable.

T0 = [-49;-45;-19;-20;30;30;100;98;238;239;350;349];
Y  = [0;0;0;0;12;8;48;44;46;34;34;40];
% And this is the code to find the fitted curve:
lb = [];
ub = [];
% Starting point
x0 = [10;10;10;10];  
F = @(x) (x(1) + x(2)*tanh((x(3) - T0)/x(4)) );
Fobj = @(x,T0) F(x); 
options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt');   
[x,resnorm,residual,exitflag,output,lambda,jacobian] = lsqcurvefit(Fobj,x0,T0,Y,lb,ub,options);

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

[Ypred,delta] = nlpredci(Fobj,T0,x,residual,'Jacobian',jacobian);

figure
plot(T0, Y,'p')
hold on
plot(T0, Ypred,'-r', T0,delta*[-1 1]+Ypred, '--r')
hold off
grid
legend('Data', 'Fitted Regression', '95% Confidence Limits', 'Location','best')

.

[Khadija]

Hello Mr. Sniper, I am working on some code and other data, I am trying to determine a shaded area. of 95% confidence interval. I am trying to understand the last program that you corrected me to do this; does the function 'nlpredci' give a confidence interval?

if we try to do the process with two curves at the same time, will we use the same function?

[Star Strider]

@Khadija — The nlpredci function returns tthe prediction interval, not the confidence interval. The two are similar however they are definitely not tthe same, with the prediction interval being ‘wider’ the the confidence interval. (I only discovered this difference recently.)

[Khadija]

How can I put the matrix of data in nlpredci?

[Star Strider]

Use the procedures described in the documentation for nlpredci.