Multiple Linear Regression
apache-commons, linear-regression, math
Solution
If you do not know the covariance between the errors you can take an iterative approach. You would first use Ordinary Least Squares, calculating the errors, and the covariances between the errors. You would then apply the GLS using the calculated covariance matrix and re-estimate the covariance matrix. You would continue iteration using GLS with the new covariance matrix until you have a convergence. Here is a link (.pdf warning) to an example of this method as well as a related discussion of Weighted and Iteratively Weighted Least Squares where you don't have a correlation between the errors as assumed in the GLS.
Problem
I am trying to use GLSMultipleLinearRegression (from apache commons-math package) for multiple linear regression. It is expecting a covariance matrix as input -- I am not sure how to compute them. I have one array of dependent variables and 3 arrays of independent variables. Any idea how to compute the covariance matrix? Note: I have 200 items for each of the 3 independent variables Thanks Bharani