determine the values of 2 unknowns through nonlinear regression and predict value of equation

I have to determine the value of 2 unknowns a and b through nonlinear regression and predict the value of the equation y for x=2.6

the equation is y=((a+sqrt(x)./(b.*sqrt(x))).^2). i looked through my class pdf's and i found nothing related to non linear regression and searched on youtube found nothing helpful . Any clues please ? or links to helpful locations websites or mathworks that might contain info . I don't know where to search anymore .

[Ameer Hamza]

Is the equation y=((a+sqrt(x)./(b.*sqrt(x))).^2) correct?

[Opariuc Andrei]

this is the equation i put the . while trying other stuff

[Ameer Hamza]

For this equation, the correct is

y=((a+sqrt(x))./(b.*sqrt(x))).^2

Answer 1

[Ameer Hamza]

There are several ways to do nonlinear regression for a given model in MATLAB. If you have the optimization toolbox, then you can use lsqcurvefit(): https://www.mathworks.com/help/releases/R2020a/optim/ug/lsqcurvefit.html or lsqnonlin(): https://www.mathworks.com/help/releases/R2020a/optim/ug/lsqnonlin.html

fit(): https://www.mathworks.com/help/releases/R2020a/curvefit/fit.html from Curve fitting toolbox can also be used.

[Opariuc Andrei]

i'm stuck ,what am i doing wrong ?

.x=2.6;

y=@(a,b)((a+sqrt(x))./(b.*sqrt(x))).^2;

%% calculus

[a,b,y]=lsqnonlin(y,x)