(3) Finally, I would like to standardize the regressors (not the dependent variable) in my dataset, such that each regressor has mean 0 and standard deviation of 1. Is there a "summary way" to do this e.g. by declaring the dataset to be a matrix, then operating on this matrix using some matrix operators?

I guess you could do this by using the "meanc" and "sdc" commands.

Or, better try the following script

<hansl>

open australia.gdt
matrix my_std_matrix = {}

loop foreach i PAU..IUS
    mymean = mean($i)
    mysd = sd($i)
    my_std_series = ($i - mymean)/mysd
    my_std_matrix = my_std_matrix ~ {my_std_series}
endloop