create a multivariable regression function in matlab without statistics toolbox in matlab

To create a multivariable regression function in MATLAB without using the Statistics Toolbox, you can use the matrix algebra approach. Here's a step-by-step guide:

1. Prepare your data:

   • Create a matrix X containing the independent variables/features. Each row represents a different observation, and each column represents a different feature.
   • Create a vector y containing the dependent variable/target variable. Each element of y corresponds to an observation in X.

2. Add a column of ones to X:

   main.m
   X = [ones(size(X, 1), 1), X];
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3. Calculate the regression coefficients:

   main.m
   % B = inv(X' * X) * X' * y
   B = (X' * X) \ (X' * y);
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4. Use the regression coefficients to make predictions:

   main.m
   y_pred = X * B;
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5. Access the regression coefficients:

   • The first element of B will be the intercept or bias term, and the remaining elements will be the coefficients for each independent variable.

Note: This approach assumes that the matrix X' * X is invertible. If it isn't, you may need to use alternative methods, such as pseudoinverse or regularization techniques.

Example:

main.m
% Sample data
X = [1, 2; 1, 3; 1, 4];  % Features (two variables)
y = [3; 4; 5];           % Target variable

% Add a column of ones to X
X = [ones(size(X, 1), 1), X];

% Calculate the regression coefficients
B = (X' * X) \ (X' * y);

% Make predictions
y_pred = X * B;

% Access the regression coefficients
intercept = B(1);
coefficients = B(2:end);
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This method allows you to perform multivariable regression without relying on the Statistics Toolbox. However, keep in mind that the Statistics Toolbox provides additional functionality and statistical measures that may be useful for analyzing and interpreting your regression model.