Every specimen sits some vertical distance from your rule — that gap is its residual. Square the residual and you get a literal square of glass; the balance weighs their total area. That total is the sum of squared errors, SSE.
The least-squares line is simply the one rule that makes the glass lightest — no other line gives a smaller total area. That is exactly what “least squares” means, and why the balance can never tip past level.
Because you square each gap, a big miss weighs far more than a small one. So a single far-off specimen — an outlier with leverage out near the edge — can drag the whole best-fit line toward itself and even flip its slope.
R² reports how much of the specimens' up-and-down scatter the best line explains: near 1 when they hug a line, near 0 when they are almost pure noise.
The balance jammed mid-weighing. The lesson continues without it — everything you have learned so far is safe.