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I need to run a multiple regression in some limited software that cannot preform any matrix calculations. I am not so good at deriving these on my own and would love some assistance.

I need something similar to these 2 walkthroughs but for a model containing 3 input variables.

https://www.statology.org/multiple-linear-regression-by-hand/

https://www.statology.org/linear-regression-by-hand/

Ex: for simple linear regression b0 = [(ΣY)(ΣX2) – (ΣX)(ΣXY)] / [n(ΣX2) – (ΣX)2] Something like this but for all coefficients for a model with 3 input variables and an intercept.

User1865345
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tmuh
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  • What software are you using? – Demetri Pananos Aug 31 '23 at 23:42
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    You definitely don't want formulas: you want algorithms. There are many of them. Among the simplest are the sequential ones, such as given at https://stats.stackexchange.com/a/71257/919 or https://stats.stackexchange.com/a/166718/919. – whuber Aug 31 '23 at 23:44

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While you can definitely devise a formula, as whuber asserted in the comment above, an efficient algorithm rather than running a formula as a code would be preferable. Nevertheless, if you want to proceed in that vein, check on this Stat.SE post.

Any such algorithm would be thematically based on Frisch–Waugh–Lovell theorem. ESL advocates the algorithm of regression by successive orthogonalization, which has been explained in this Stat.SE post. Depending on your programming language, you can write the code based on this algorithm.

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