<p>I think it is quite obvious (so long as you read it in its entirety) that <a href="https://stats.stackexchange.com/questions/196807/answers-to-3d-linear-regression-in-closed-form">this</a> question has incorrectly been marked as duplicate. It is worth reading the comments too.</p>

<p><strong>EDIT:</strong> Just to be clear, my question requests an answer that gives values of A,B and C explicitly rather than implicitly. Some readers may think that an implicit answer is just as good, but the implicit ones leave me with three simultaneous equations to solve. This is doable, but in practice its quite difficult to do without a chance of making a mistake.</p>
