Without using matrices

How can you derive OLS estimators in multiple regression ?

  • 2
    $\begingroup$ Well, you can write out each equation of the normal equation separately and then try and solve by plugging in. It won't be nice though, and, imo, quickly convince anybody that investing some time into learning matrix algebra is worth it. $\endgroup$ Commented Apr 1, 2022 at 7:13
  • $\begingroup$ Hi @Iam Shawnie. I don't know your background, but OLS is taught in undergrad econometrics without using matrices. Therefore, books like Principles of Econometrics by Hill et al, show these kinda derivations (with only two covariates max, probably). Also, Ben Lambert's undergraduate econometrics YouTube series is likely to show this kinda derivation. Very good videos, but I haven't watched them in a while. $\endgroup$
    – EB3112
    Commented Apr 1, 2022 at 8:10
  • $\begingroup$ stats.stackexchange.com/questions/196807/… $\endgroup$
    – whuber
    Commented Apr 1, 2022 at 12:41
  • 2
    $\begingroup$ What do you want to use? Lots of indices? Geometry? Abstract geometry? Vector arithmetic? Ruler and compass? Complex numbers? Something else? $\endgroup$
    – whuber
    Commented Apr 1, 2022 at 12:48


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