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Does anyone know if there's a general expression for the jth slope coefficient from a multiple regression with K independent variables, in terms of variances and covariances? Obviously, the expressions in the case where K=1 and K=2 are straightforward, but is there a more general expression?

And yes, I know how to find the betas using matrix algebra ... but that's not appropriate in the context I'm looking at.

Stadius
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  • Can't formulate an answer right now, but look into the relationship between $\beta$ coefficients and partial correlation. – Firebug Apr 12 '17 at 17:01
  • The "more general expression" will be equivalent to the [standard matrix formulas.](http://stats.stackexchange.com/questions/107597/) People have asked this question here for the cases $K=2$ and $K=3$ (see http://stats.stackexchange.com/questions/196807 for instance), and you will find various answers, but somewhere we need to draw the line and insist that if you really, really want to write a formula without matrix notation, then do it yourself. See [Cramer's Rule](https://en.wikipedia.org/wiki/Cramer%27s_rule). – whuber Apr 12 '17 at 22:10

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