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Suppose I have a multiple linear regression model $$ Y=\beta_0+\beta_1X_1+\cdots+\beta_pX_p+\epsilon$$ How can I obtain the regression coefficients $\hat{\beta_i}$ by fitting just a series of simple linear regression models (additionally using sample means of the response/predictor variables if needed)?

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marked as duplicate by whuber regression Feb 28 at 14:56

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  • $\begingroup$ Why would you? If this is homework, please use the self-study tag. Hint: you could search this site for "Frisch Waugh Lovell". $\endgroup$ – Christoph Hanck Feb 28 at 11:02
  • $\begingroup$ Alternatively, look into Gram-Schmidt orthogonalization. $\endgroup$ – Glen_b Feb 28 at 12:12