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I am very new to the concept of regression. While going through an R output for a multiple regression I came across a set of estimates for the slope and got interested to solve for the same. for 2 independent variables the formula derived from the covariance matrix works fine but the trouble starts while solving it for more than 2 variables. Can some one help me with how the formula is extended in case of more than 2 IVs? Sorry for this naive question.But I am very curious about the fact. The formula that I have been following is- β1=Cov(y,x1)var(x2)−Cov(y,x2)Cov(x1,x2)/var(x1)var(x2)−Cov(x1,x2)2

For three IVs, does the following formula make any sense? β1=Cov(y,x1)var(x2)var(x3)−Cov(y,x2)Cov(y,x3)Cov(x1,x2)Cov(x1,x3)cov(x2,x3)/var(x1)var(x2)var(x3)−{Cov(x1,x2)Cov(x2,x3)Cov(x1,x3)}2

It will be of huge relief if someone could correct me. Thank YOU.

deyatima ghosh
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  • If your concern focuses on writing out the matrix formulas, component by component, then https://stats.stackexchange.com/questions/196807 might be of some help. – whuber Jun 19 '17 at 14:14

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