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I understand how to perform a least means regression of a given set of $x$ points to approximate a line that best fits them. In this case I observe a set of $x$ inputs and y corresponding outputs. Then I can create$ a \hat y = m\hat x+ b$ which is a line that best fits the $x$ and $y$ I observed.

Now let's suppose that I do this experiment several times. Now I have a matrix of $X $observations and a matrix of Y corresponding outputs. How would I find the $\hat y = m\hat x+ b$ that best fits all observations?

Тyma Gaidash
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CakeMaster
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  • You have a long list of x values and a long list of y values. – Paul May 26 '23 at 19:13
  • The general case of linear regression is that of projection. Given $X,$ you consider $V$ the image space of $X$ (i.e. "column space") and $P_X$ the orthogonal projector onto $V.$ The multiple linear regression is then $P_X(Y).$ – William M. May 26 '23 at 19:35
  • Please use \hat x for $\hat x$ otherwise it looks like exponentiation – Тyma Gaidash May 26 '23 at 22:39

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