Generate random errors for data with specific covariance matrices

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Mary Tavoosi
Mary Tavoosi 2021-10-3
评论： Mary Tavoosi 2021-10-3
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?

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the cyclist
the cyclist 2021-10-3
If you have the Statistics and Machine Learning Toolbox, you can generate correlated normal variables with the mvnrnd function.
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the cyclist
the cyclist 2021-10-3
Ran in:
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

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