Least squares finds the one line that makes the total area of the little squared-residual panes as small as possible. A lovely consequence: the fitted line always pivots through the centroid (x̄, ȳ) — a beam on a fulcrum.
Not every point pushes on that beam equally. A point's leverage h = 1/n + (x−x̄)²/Sxx depends only on where in x it sits, not on its y. Points far out on the x-axis have long moment arms; points near the centre have almost none.
Influence marries leverage to residual. Cook's distance asks how far the whole fit shifts if you delete one point; a value past 1 flags a specimen that is steering the line by itself.
This is why a wild y-outlier in the middle barely tilts the beam, while a mild point at the edge can commandeer it — and why a triumphant R² can be a lie, propped up entirely by a single far-out specimen (Anscombe's fourth quartet).
The bench's balance instrument jammed mid-measurement. The lesson continues without it — everything you have learned so far is safe.