Change initial conditions to maximize Rsquared

For example is there a way to tell matlab + or - these varaibles (X,Y,Z) by 0.001 as needed to maxamize the R squared value??

Such as a while loop that looks like this? this is a made up script for an example

X1 = 1

Y1 = 1

Z1 = 1

X2 = 1

Y2 = 1

Z2 = 1

Fit = fitlm(A,B);

R2 = Fit.Rsquared.Ordinary; ( gets an R squared lets assume not 1)

while R2 < 0.8

dx = 0.001 ( I want this dx to be + or - 0.001 somehow in order to maxamize R squared (R2))

X1 = X1 +dx

Y1 = Y1+dz

Z1 = Z1+dx

..... same for X2 Y2 Z2

A = sin(X1+Y1+Z1)

B=sin(X2+Y2+Z2)

Fit = fitlm(A,B);

R2 = Fit.Rsquared.Ordinary;

end

Answer 1

[Deepak]

Hi @Wilfredo Huaman,

I understand that you want to adjust variables (X1, Y1, Z1, X2, Y2, Z2) by small amounts (±0.001) in order to maximize the R-squared (R²) value from a fitlm regression. The goal is to iteratively tweak these variables until R² exceeds a target threshold, such as 0.8.

You can achieve this using a loop that tests small ±0.001 changes and updates the variables when an improvement in R² is found. Below is a sample MATLAB code to achieve the same. This approach iteratively improves R² by testing ±dx steps.

X1=1; Y1=1; Z1=1; X2=1; Y2=1; Z2=1; dx=0.001; bestR2=0;
while bestR2 < 0.8
    improved = false;
    for s = [-1 1]
        A = sin((X1+s*dx)+(Y1+s*dx)+(Z1+s*dx));
        B = sin((X2+s*dx)+(Y2+s*dx)+(Z2+s*dx));
        R2 = fitlm(A', B').Rsquared.Ordinary;
        if R2 > bestR2
            [X1,Y1,Z1,X2,Y2,Z2] = deal(X1+s*dx, Y1+s*dx, Z1+s*dx, X2+s*dx, Y2+s*dx, Z2+s*dx);
            bestR2 = R2; improved = true; break;
        end
    end
    if ~improved, break; end
end

Please find attached the documentation of function used for reference:

fitlim: www.mathworks.com/help/stats/fitlm.html

I hope this assists in resolving the issue.