ridge regression of x and y in matlab

To perform ridge regression of x and y in Matlab, you can use the ridge function from the Statistics and Machine Learning Toolbox. Ridge regression is a regularization technique that helps prevent overfitting by adding a penalty term to the regression equation.

Here is a basic example of how to use the ridge function:

main.m
% Generate some example data
x = [1, 2, 3, 4, 5];
y = [2, 4, 6, 8, 10];

% Perform ridge regression
lambda = 0.1;  % Regularization parameter
[beta, bint, r, rint, stats] = ridge(y, x, lambda);

% Display the results
disp("Ridge Regression Results:")
disp("-----------------------------------------")
disp("Estimated Coefficients (Beta):")
disp(beta)
disp("Confidence Intervals:")
disp(bint)
disp("Residuals:")
disp(r)
disp("Residuals Confidence Intervals:")
disp(rint)
disp("Model Statistics:")
disp(stats)

% Plot the original data points and the fitted ridge regression line
plot(x, y, 'o', 'DisplayName', 'Data')
hold on;
plot(x, x*beta, 'r', 'DisplayName', 'Fitted Ridge Regression Line')
hold off;
title('Ridge Regression')
xlabel('x')
ylabel('y')
legend('Location','northwest')
grid on;
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This example generates some artificial data, performs ridge regression with a regularization parameter (lambda) of 0.1, and displays the estimated coefficients, confidence intervals, residuals, residuals confidence intervals, and model statistics. It also plots the original data points and the fitted ridge regression line.

You can adjust the lambda value to control the amount of regularization in the ridge regression.

Note: The ridge function assumes that the input x is a matrix with each column representing a different predictor variable, and y is a vector of response variable values.

Make sure you have the Statistics and Machine Learning Toolbox installed and loaded in Matlab in order to use the ridge function.