<p>I am happy to debate this, and would not be offended to be found on the wrong side of the debate.  But let's get the facts into the open.  For the record, here are the explanations I provided for why the question was closed.</p>
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<p>I realize the duplicate is only for three predictors. [I meant to write &quot;two&quot;, btw.] However, there has to be an end somewhere, lest we accumulate a growing list of versions of this question where &quot;two&quot; becomes &quot;three&quot; becomes &quot;four&quot; <em>ad infinitum</em> and <em>ad nauseam.</em> At some point--and I sincerely think it has occurred by the time there are two independent variables (which, with a constant, actually make three)--it becomes clear that these questions are asking for painful elaboration of the complicated formulas lurking behind the matrix equations, and as such they have no interest for statistics or computation.</p>
<p>Generalization is incredibly obvious: use matrices. If you really want to unfold the formulas for matrix inversion into sums and products, then go ahead. But I stand by my opinion that this is of no interest or use in statistics or machine learning.</p>
<p>You might find it informative, as well as useful, to know that as soon as you have a formula for even one independent variable, you can leverage it into an algorithm for any number of independent variables. I have explained this in answers at stats.stackexchange.com/questions/46185 and stats.stackexchange.com/questions/17336, <em>inter alia.</em> I'm not saying there's anything the matter with your question or that it's somehow stupid--it's not. It's just that it makes no sense--and would even be counterproductive--to attempt an answer in light of the facts I have brought forward.</p>
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<p><strong>My concern is a simple one:</strong> if we do not allow <em>trivial</em> duplications of this sort to count as duplicates, then we risk encumbering the site with redundant answers.  How should we respond to the hypothetical person who says their question about how to apply a t-test differs from one exactly like it (involving a sample size of <span class="math-container">$98$</span>) because they have a dataset of size <span class="math-container">$99$</span> instead of <span class="math-container">$98$</span>?  I appeal to your reason and common sense: <em>if anyone capable of understanding the question as asked could reasonably be expected to recognize that a purported duplicate is purely and obviously a mathematical variation of the same question, then the purported duplicate counts as an &quot;exact&quot; duplicate.</em></p>
<p>(The present case goes beyond this fundamental concern insofar as I see no interest for statistics or machine learning in writing out the formulas separately for matrix products and inverses for two, three, four, ... dimensions.  Anyone can look those up and apply them as they see fit.  But that's not the basic, original reason for voting to close this question.)</p>
<p><strong>Another twist in this case</strong> is the artificiality of demanding that answers not use matrix notation.  I view such questions as being similar to others that ask for some algorithm or procedure <em>that has already been given elsewhere on the site,</em> but the OP demands an answer in some other language. We close those questions, too.</p>
<p><strong>Please note that I am not trying to preclude related questions.</strong>  This one could be made on topic in numerous ways, such as by asking what are efficient methods to compute OLS estimates; why do people not use formulas like Cramer's Rule to compute those estimates; or even why do all explicit formulas use matrix notation?</p>
