Generate random errors for data with specific covariance matrices

Hello

I have simulated 450 data for a linear regression model with 5 independent variables and a dependent variable (y=a*x1+b*x2+c*x3+d*x4+e*x5+f). Each of these data has specific weights(Wy, Wx1, Wx2, Wx3, Wx4, Wx5) . Now I want to add a random error with a mean of zero and variance (for example Sigma*inv(W) ) of each variables to this data. How can this be done?

Answer 1

[the cyclist]

If you have the Statistics and Machine Learning Toolbox, you can generate correlated normal variables with the mvnrnd function.

[Mary Tavoosi]

Thanks for your answer. I think Mvnrnd function use a variance for all variables I want each variable has a special variance. Is it true?

[the cyclist]

If you read the documentation carefully, you will see that you can specify the full variance matrix. Here is an example:

N = 1000000;
mu = [0; 0; 0];
sigma = [1.0 0.5 0.5;
         0.5 0.9 0.7;
         0.5 0.7 0.7];
x = mvnrnd(mu,sigma,N);

var(x)

ans = 1×3

0.9983 0.8980 0.6988

[Mary Tavoosi]

thank you