$1-$Derive equation $2\mathrm{.}17$

where $\stackrel{}{x}={\displaystyle \underset{t}{\overset{?}{}}}\frac{x^t}{N}\frac{,}{b}ar(r)={\displaystyle \underset{t}{\overset{?}{}}}\frac{r^t}{N}.$ The line found is shown in figure $1\mathrm{.}2.$

If the linear model is too simple, it is too constrained and incurs a

large approximation error, and in such a case, the output may be taken

as a higher$-$order function of the input, for example, quadratic

$(2\mathrm{.}17)g(x)=w_2{x}^2+w_{1}x+w_0$

where similarly we have an analytical solution for the parameters. When

the order of the polynomial is increased, the error on the training data de$-$

creases. But a high$-$order polynomial follows individual examples closely

instead of capturing the general trend $($see the sixth$-$order polynomial in

figure $2\mathrm{.}9),$ so we should be careful when fine$-$tuning the model complex$-$

ity to the complexity of the function underlying the data.