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In a regression model function, What does this absolute value notation mean?

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Ibrahim Abouhashish
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    For $n$-dimensional vectors $||\cdot||_2$ typically represents the Euclidean, or standard, norm. $||v||_2 = \sqrt{v_1^2+v_2^2+...+v_n^2}.$ – D.B. Jan 14 '19 at 21:27
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    $||x||2 = \sqrt{\sum{i=1}^{n}{x_i^2}}$ – lightxbulb Jan 14 '19 at 21:27
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    Even more generally, $|x|p = \left(\sum{i=1}^n |x_i|^p\right)^{1/p}$ is the $p$-norm for $\ell_p$ space which Euclidean norm/space is an example of. In your specific example, the super-script $2$ is there as a power so $|x|_2^2 = x_1^2+x_2^2+\dots+x_n^2$ – JMoravitz Jan 14 '19 at 21:31
  • @D.B. considering x is also a matrix, what would $ x^{(n)} $ mean – Ibrahim Abouhashish Jan 15 '19 at 19:44
  • I actually think that $x^{(n)}$ and $y^{(n)}$ are just vectors. The quantity you have shown looks like a measure of the error between your data $y^{(n)}$ and your regression model. – D.B. Jan 17 '19 at 05:30

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