Write MATLAB code that implements the parametric bootstrap.Test it using the forearm data.Assume that the normal distribu-tion is a reasonable model for the data.Use your code to get abootstrap estimate of the standard error and the bias of the coeffi-cie

Sure, here is the MATLAB code that implements the parametric bootstrap:

% Load forearm data
load forearm

% Define function that fits linear regression model and returns coefficient estimates
fit_lm = @(x, y) [ones(size(x)), x] \ y;

% Define number of bootstrap samples
B = 1000;

% Define empty arrays to store bootstrap estimates
beta0_boot = zeros(B, 1);
beta1_boot = zeros(B, 1);

% Compute original coefficient estimates
beta_orig = fit_lm(forearm(:, 1), forearm(:, 2));

% Compute standard deviation of residuals
resid_std = std(forearm(:, 2) - beta_orig(1) - beta_orig(2) * forearm(:, 1));

% Perform bootstrap
for i = 1:B
    % Generate bootstrap sample
    y_boot = beta_orig(1) + beta_orig(2) * forearm(:, 1) + randn(size(forearm(:, 1))) * resid_std;
    
    % Fit linear regression model to bootstrap sample
    beta_boot = fit_lm(forearm(:, 1), y_boot);
    
    % Store bootstrap estimates
    beta0_boot(i) = beta_boot(1);
    beta1_boot(i) = beta_boot(2);
end

% Compute bootstrap standard errors and bias
beta0_se = std(beta0_boot);
beta1_se = std(beta1_boot);
beta0_bias = mean(beta0_boot) - beta_orig(1);
beta1_bias = mean(beta1_boot) - beta_orig(2);

% Display results
disp(['Bootstrap standard error of intercept: ', num2str(beta0_se)]);
disp(['Bootstrap standard error of slope: ', num2str(beta1_se)]);
disp(['Bootstrap bias of intercept: ', num2str(beta0_bias)]);
disp(['Bootstrap bias of slope: ', num2str(beta1_bias)]);

This code fits a linear regression model to the forearm data using the `fit_lm` function, which simply calls the backslash operator to perform the least squares optimization. It then defines the number of bootstrap samples `B`, and initializes empty arrays to store the bootstrap estimates.

The code then computes the standard deviation of the residuals of the original model, which is used to generate the bootstrap samples. It then iterates over `B` bootstrap samples, generating a new set of observations by adding Gaussian noise to the original predictions based on the standard deviation of the residuals. It fits a new linear regression model to each bootstrap sample, and stores the resulting coefficient estimates.

Finally, the code computes the standard errors and bias of the bootstrap estimates, and displays the results.