How to do a stepwise multivariate regression analysis with random variables

Hey folks!

I would like to run a stepwise multivariate regression analysis with random variables using:

rng(10, 'twister')

I tried to to create 100 normally distributed random variables with 100 observations per variable.

Runned it like this format but couldn't do it: y = a + b1 * x1 + b2 * x2 + ... + b100 * x100 + u

There 5 best explanatory variables should be kind of picked and used to run another regression:

y = a + b1 * z1 + b2 * z2 + ... + b5 * z5 + v

I would very much appreciate any input and help! Thanks!

Answer 1

[Ronit]

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:

1. Setup the environment and generate data.
2. Run stepwise multivariate regression - using “stepwiselm”.
3. Identify the best explanatory variables - You can extract these variables directly from the model.
4. 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:

https://www.mathworks.com/help/stats/stepwiselm.html

https://www.mathworks.com/help/stats/fitlm.html

Hope this helps!