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I have $n$ observations of $m$ variables. I would like to regress each of the $m$ variables against the other $m-1$ variables.

Is there a more efficient way of doing this than running $m$ regressions?

Jack Black
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  • "Regress"... What statistic(s) do you want exactly? – ttnphns Mar 05 '20 at 19:52
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    I believe that once you have computed the full covariance matrix, you can combine the $O(m^2)$ method of updating the inverse of the covariance matrix (https://stats.stackexchange.com/questions/196814) with the $O(m^2)$ solution in terms of the inverse covariance at https://stats.stackexchange.com/questions/107597. Whether this is more efficient depends on how you are running the $m$ regressions. – whuber Mar 05 '20 at 21:08

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