Cook's Distance

A point can be a statistical outlier — far from the other data — without changing the regression line at all, if it sits close to where the line already predicts. Cook's distance answers a more useful question: how much would every fitted value in the regression shift if this one observation were removed and the model refit? It combines two things that each matter separately but do the real damage only together: how far the point's $x$-value sits from the center of the other $x$'s (its leverage), and how badly the model mispredicts it (its residual). A point with high leverage and a small residual, or a large residual at low leverage, produces only a modest Cook's distance; a point with both is the one dragging the whole fitted line toward itself.

A common rule of thumb flags any observation with Cook's distance above $4/n$ (where $n$ is the sample size) for closer inspection — not automatic deletion. With $n = 50$, that threshold is $0.08$; a company-quarter observation coming in at $0.35$ is flagged as unusually influential and worth checking for a data error or a genuine one-off event before deciding whether to keep it in the sample.