Regression using Higher Order Polynomial feature $0/1$ punto $($calificado$)$ Assume we have n data points in the training set $\{($x$^($t$),$ y$^($t$))\}\_$t$=1,...,$ n where $($x$^($t$),$ y$^($t$))$ is the t$-$th training example: A biochemist is considering the depicted data and we're helping them. We want to find a non$-$linear regression function f that predicts y from x$,$ given by

f$($x ; $\backslash$theta $,\backslash$theta $\_0)=\backslash$theta $($x$)+\backslash$theta $\_0$

where $($x$)$ is the polynomial feature vector that includes all and only the monomials of degree at most k $($in this case, since x has dimension $1,$ this means $$ has k$+1$ components; the degree$-0$ component is redundant with the bias term $\backslash$theta $\_0,$ but that doesn't matter for this problem$).$ What degree k would you recommend the biochemist use? Note that this is a soft, not$-$completely$-$mathematical question, much like the question, 'Does Louisiana look more like a boot or a mitten?$\text{'}-$ there's consensus here among folks who know the terms involved, even though it's a soft question. Common sense and human experience are important in ML engineering, so this question is fair game.