design the function function out = mse_vs_m(x_tr, t_tr, x_te, t_te) that uses all given samples in the split data setsand then computes the empirical 5 mse test loss in matlab

main.m
function out = mse_vs_m(x_tr, t_tr, x_te, t_te)
% Calculates the mean squared error for different model complexities
% using a training set and a testing set

% Number of samples in the training set
n_tr = size(x_tr, 1);

% Number of samples in the testing set
n_te = size(x_te, 1);

% Maximum model complexity (adjust as needed)
M = 10;

% Preallocate arrays to store the MSE values
mse_train = zeros(M, 1);
mse_test = zeros(M, 1);

for m = 0:M-1
    % Fit a polynomial regression model of degree m to the training data
    X_tr = [ones(n_tr, 1), x_tr.^1, x_tr.^2, ..., x_tr.^m];
    w = (X_tr' * X_tr) \ (X_tr' * t_tr);
    
    % Evaluate the model on the training set and calculate the MSE
    y_tr = X_tr * w;
    mse_train(m+1) = mean((y_tr - t_tr).^2);
    
    % Evaluate the model on the testing set and calculate the MSE
    X_te = [ones(n_te, 1), x_te.^1, x_te.^2, ..., x_te.^m];
    y_te = X_te * w;
    mse_test(m+1) = mean((y_te - t_te).^2);
end

% Store the results in a struct
out = struct('mse_train', mse_train, 'mse_test', mse_test);
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