How do I find Rsquared?

Hello! Please, I need help. Tried everything and couldn't do it.

I have 2 vectors of values:

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 I need to use the equation F=A+B*tanh((T-T0)/C) to fit these points. So I'm using the optimoptions to find the best fit:

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);

I know (using the Curve Fit Toolbox) that the values of x are supposed to create a curve with Rsquared = 0.9585, but even using the function corrcoef I can't find this R squared.

Can anybody, please help?

Answer 1

[Sulaymon Eshkabilov]

Hi,

Here is the quick solution:

% 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);
FM = (x(1) + x(2)*tanh((x(3) - T0)/x(4)) );
plot(T0, Y, 'ro', T0, FM, 'b--')
RSS = sum((Y-FM).^2);
TSS = sum((Y-mean(Y)).^2);
R_sq = 1-RSS/TSS;
fprintf('R square  = %1.3f \n', R_sq)

Good luck.

[Renan Fraga]

Thank you so much!

[Sulaymon Eshkabilov]

You are most welcome! It is just a pleasure!