Hello,
To conduct a stepwise multivariate regression analysis with random variables as you have described, the process involves generating random variables, running the stepwise regression to identify 5 best variables, and then running another regression with the selected variables. Following is the overview of the steps:
- Setup the environment and generate data.
- Run stepwise multivariate regression - using “stepwiselm”.
- Identify the best explanatory variables - You can extract these variables directly from the model.
- Run another regression with selected variables.
Following is a sample code for above mentioned steps:
% Initialize the random number generator for reproducibility
rng(10, 'twister');
X = randn(100, 100); % 100 observations of 100 variables
% For simplicity, let's assume y is a linear combination of some variables in X plus some noise
coefficients = randn(100, 1); % Random coefficients for the 100 predictors
noise = randn(100, 1); % Random noise
y = X * coefficients + noise; % Linear model
% Running stepwise linear regression
model = stepwiselm(X, y, 'linear', 'Criterion', 'bic', 'Upper', 'interactions', 'Verbose', 2);
% For example, let's say the indices are 1, 2, 3, 4, 5 for simplicity
Z = X(:, [1, 2, 3, 4, 5]);
% Run the regression with the selected variables
finalModel = fitlm(Z, y);
For more information regarding the models used, refer to the following links:
Hope this helps!
