$5.$ Linear Regression and RegularizationFor each of the datasets below, provide a simple feature mapping o such that the transformed data $(($x$),$y$))$would be well modeled by linear regression. $140120100$ Which feature mapping is appropriate for the above model? exp $($x$)$ log $($x$)$Which feature mapping is appropriate for the above model? $($x$)$ x$+$sign $()($x$)$x$-$sign $($x$)($x$)=$ x$-$sign $()$ x$/$sign $($x$)($x$)**$s$...$Consider fitting a l$2-$regularized linear regression model to data $($x$(1),$ y$1)),...,($e$($m$),$ y$($n$))$ where ae$,$yt $$ R are scalar values for each t $1,.,$n$.$ To fit the parameters of this model, one solves L $(0,00)$ min eER, ER where $($y$)-$r$())$ L $(0,00)=$ t$-1$ Here A$0$ is a pre$-$specified fixed constant, so your solutions below should be expressed as functions of referred to as ridge regression and the data. This model is typically Write down an expression for the gradient of the above objective function in terms of e$.$ Important: If needed, please enter respectively $(...)$ as a function sum$\_$t$(...),$ including the parentheses. Enter and y as xft$\}$ and yft$,$ Write down an expression for the gradient of the above objective function in terms of eFind the closed form expression for eo and e which solves the ridge regression minimization above. Assume $0$ is fixed, write down an expression for the optimal o in terms of $0,$ x$),$ y$($t$),$ n$.$ Write down an expression for the optimal $($defined below$)$ in terms of $),$y$(),$ n$,$ A and $1$ Note: To simplify your expression, please use enter this as barx. Now after the optimal e is obtained, you can use it to compute the optimal $0$