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I want to show that the slope coefficient for the jth regressor for $i = 1, \dots, 2$ and $j = 1, \dots, k$ is given as

$$ b_j = \frac{Cov(y_j, u{_{ji}})}{Var(u_{ji})}$$

where $u_{ji}$ is the residual from a regression of $x_{ji}$ on all other covariates.

Tv_2020
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  • If this is for self study, you should probably tag it as such ([tag:self-study]) in order to get better guidance here. – chl Nov 15 '20 at 12:43
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    I think you shoul remove the j index on y. Also maybe bother to write up the model. I am assuming we are in the setting of linear regression. – Jesper for President Nov 15 '20 at 13:03
  • This is a FAQ: see https://stats.stackexchange.com/search?q=regression+slope+formula. – whuber Nov 15 '20 at 16:02

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