 Solution

The dashed curves are contours of constant Cook's distance, labelled 0.5 and 1, in the plot of standardized residual against regression leverage. Writing $h_{ii}$ for the diagonal of the hat matrix, $s^2$ for the residual variance estimate, and $p=8$ for the number of fitted coefficients,Thus a contour $D_i=d$ has $r_i=\pm \sqrt{dp(1-h_{ii})/h_{ii}}$. On the actual PDF plot, observation 579 has leverage about 0.084 and standardized residual about $-8$, lying beyond the $D=0.5$ contour and below $D=1$ in influence magnitude, approximately $D\simeq 0.7$ to $0.8$ from the plotted coordinates. It is unusually light relative to its fitted log-weight and potentially influential because deleting it can materially change fitted coefficients. It warrants checking, not automatic deletion. The solid smooth red curve is distinct from the dashed Cook's distance contours.