ridge regression of x and y with fitlm in matlab

To perform ridge regression of x and y using the fitlm function in MATLAB, you can follow these steps:

1. Define your predictor variable x and response variable y.

2. Construct a design matrix X by adding a column of ones to x. This is necessary for the intercept term in the regression model.

3. Set the value of the ridge regularization parameter alpha. This parameter controls the amount of regularization applied in the ridge regression. Higher values of alpha lead to more regularization.

4. Call the fitlm function with the design matrix X, response variable y, and the 'ridge' option to perform ridge regression.

Here's an example code snippet to illustrate the steps above:

main.m
% Step 1: Define predictor and response variables
x = [1, 2, 3, 4, 5]';
y = [2, 4, 6, 8, 10]';

% Step 2: Construct design matrix X
X = [ones(size(x)), x];

% Step 3: Set ridge regularization parameter
alpha = 0.1;

% Step 4: Perform ridge regression using fitlm
lm = fitlm(X, y, 'Linear', 'PredictorVars', [2], 'intercept', false, 'Regularization', 'ridge', 'Lambda', alpha);

% Display the results
disp(lm)
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In this example, we first define x and y as column vectors. Then we create the design matrix X by adding a column of ones to x. We set alpha to 0.1, and finally call fitlm with the necessary options to perform ridge regression. The resulting linear model (lm) will contain the ridge regression coefficients and other information.

Note: Make sure you have the Statistics and Machine Learning Toolbox installed in MATLAB to use the fitlm function.