= Solution
The solid curve is the <test error>
$$
\frac1n\|Y^*-\widehat Y_\lambda\|_2^2,
$$
and the dashed curve is the <training error> $n^{-1}\|Y-\widehat Y_\lambda\|_2^2$. As the horizontal coordinate tends to $+\infty$, $\lambda\to\infty$, so every penalized slope tends to zero and $\widehat Y_\lambda\to\overline Y\mathbf1$. The two limits are therefore
$$
\frac1n\|Y^*-\overline Y\mathbf1\|_2^2
\quad\hbox{and}\quad
\frac1n\|Y-\overline Y\mathbf1\|_2^2,
$$
respectively.
As the horizontal coordinate tends to $-\infty$, $\lambda\downarrow0$ and the fit approaches the <ordinary least squares> fit $H_0Y$. Hence the solid curve tends to $n^{-1}\|Y^*-H_0Y\|_2^2$, which the plot shows is approximately $0.4$.
Back to article page