To determine the coefficient correlation for multiple series of data with four variables

I have the follwoing three sets of data with four data varialbes from experiment work. where Ta, Tw and Tw2 are indepedent variables and p is dependent varialbes.

Ta = [25.25,25.6,24.67,24.03,23.87; 21.89,21.26,21.18,21.29,21.33; 20.42,20.36,20.47,20.47,20.17];

Tw = [29,31,33,36,38; 31,34,36,38,40; 32,34,36,38,40];

Tw2 = [841,961,1089,1296,1444; 961,1156,1296,1444,1600; 1024,1156,1296,1444,1600];

p = [0.46, 0.49, 0.51, 0.55, 0.57; 0.50, 0.53,0.55,0.56,0.60; 0.51,0.54,0.56,0.58,0.61];

i like to determine a single set of coeeficient correlation results out of these data based on following equation.

p = p0 + p1 (Tw) + p2 (Tw2) + p3 (Ta)

here need to determine a singel set of results for p0, p1, p2, p3.

Thank you.

Answer 1

[atharva]

Hey Sheikh Khaleduzzaman,

I understand that you need to determine a singel set of results for p0, p1, p2, p3.

you can try running the following Matlab code-

% Given data
Ta = [25.25, 25.6, 24.67, 24.03, 23.87; 21.89, 21.26, 21.18, 21.29, 21.33; 20.42, 20.36, 20.47, 20.47, 20.17];
Tw = [29, 31, 33, 36, 38; 31, 34, 36, 38, 40; 32, 34, 36, 38, 40];
Tw2 = [841, 961, 1089, 1296, 1444; 961, 1156, 1296, 1444, 1600; 1024, 1156, 1296, 1444, 1600];
p = [0.46, 0.49, 0.51, 0.55, 0.57; 0.50, 0.53, 0.55, 0.56, 0.60; 0.51, 0.54, 0.56, 0.58, 0.61];

% Reshape matrices to vectors
Ta = reshape(Ta, [], 1);
Tw = reshape(Tw, [], 1);
Tw2 = reshape(Tw2, [], 1);
p = reshape(p, [], 1);

% Create the design matrix
X = [ones(size(Ta)), Tw, Tw2, Ta];

% Fit a linear model
coefficients = X\p;

% Extract coefficients
p0 = coefficients(1);
p1 = coefficients(2);
p2 = coefficients(3);
p3 = coefficients(4);

% Display the results
disp(['p0: ', num2str(p0)]);
disp(['p1: ', num2str(p1)]);
disp(['p2: ', num2str(p2)]);
disp(['p3: ', num2str(p3)]);

This script reshapes the matrices into vectors and creates a design matrix X with columns for the constant term, Tw, Tw2, and Ta. The backslash operator (\) is then used to solve the linear system and obtain the coefficients.

Finally, the results are displayed.

I hope this helps!

[Sheikh Khaleduzzaman]

Thank you so much for your right solution! Atharva.