Residual
For a regression line ŷ = a + bx, the residual for observation (x, y) is e = y - ŷ = y - (a + bx). The sum of residuals is always zero for the least squares regression line. The sum of squared residuals is minimized.
Real World
Sports scientists at a Premier League club fit a regression line linking training hours to sprint speed; a player with an unusually large positive residual outperforms predictions, flagging exceptional natural ability.
Exam Focus
State that the sum of residuals equals zero as justification when checking your arithmetic — examiners award this explicitly.
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