To fit a linear model to the simulated data in Julia, you can use the GLM (Generalized Linear Models) package, which provides functions to perform linear regression. Here's how you can do it:

    Install the GLM package if you haven't already. Open a Julia REPL and type the following command:

using Pkg
Pkg.add("GLM")

    After installing the GLM package, you can modify your code to include the fitting of the linear model:

using StatsBase
using GLM

function simulate_data(n_samples, n_features, beta, sigma)
    """Simulates example data for a general linear model.

    Args:
        n_samples: The number of samples to simulate.
        n_features: The number of features.
        beta: The coefficient vector.
        sigma: The noise standard deviation.

    Returns:
        A tuple of (X, y), where X is the design matrix and y is the response vector.
    """

    X = randn(n_samples, n_features)
    y = X * beta + sigma * randn(n_samples)
    return X, y
    end

if __name__ == "__main__"
    n_samples = 100
    n_features = 5
    beta = randn(n_features)
    sigma = 0.1
    X, y = simulate_data(n_samples, n_features, beta, sigma)

    # Fit a linear model using GLM
    model = lm(@formula(y ~ X), DataFrame(X=X, y=y))
    coefficients = coef(model)

    println("True Coefficients: ", beta)
    println("Estimated Coefficients: ", coefficients)
    end

In the updated code, we added the using GLM statement to import the GLM package. Then, we use the lm() function from GLM to fit a linear model to the simulated data. The lm() function takes a formula and a DataFrame as arguments. The formula specifies the relationship between the response variable y and the predictor variables X. The DataFrame is constructed using DataFrame(X=X, y=y) to provide the data to the function.

After fitting the model, we print the true coefficients used to generate the data (beta) and the estimated coefficients obtained from the linear model.

To run this code, save it as a .jl file (e.g., linear_model.jl) and then run it from the command line using the julia command:
julia linear_model.jl

This will simulate the data, fit a linear model, and print the true and estimated coefficients. Note that the estimated coefficients might not perfectly match the true coefficients due to the noise introduced during data simulation.
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