Here is Octave code which produces the same covariance values as gretl:
degrees_of_freedom = cases-predictors;
coefficients = pinv(IV)*DV;
estimates = IV*coefficients;
residuals = DV-estimates;
SSres = residuals'*residuals;
residual_variance = SSres/degrees_of_freedom;
N=IV'*IV;
Ni=inv(N);
covariance_matrix = Ni*residual_variance;
From: Mario Florez Porras <mario.florez.porras(a)gmail.com>
To: gretl-users(a)lists.wfu.edu
Sent: Tuesday, August 30, 2016 4:36 PM
Subject: [Gretl-users] MLE Advanced
Anyone know how it is calculated the covariance matrix?