= Residual constraints from a bounded response
{title2=$L-\widehat y_i\le e_i\le U-\widehat y_i$}
If observed responses satisfy $L\le y_i\le U$, their <regression residuals> $e_i=y_i-\widehat y_i$ necessarily obey the displayed inequalities. Subtracting the corresponding <fitted values> proves both bounds, without a <normal distribution> or a fitted-model assumption. On a <residual-versus-fitted plot>, all points must lie between two parallel lines of slope $-1$. This is also a consistency check when $L,U$ are merely the reported observed minimum and maximum, rather than theoretical response limits. A bounded response does not itself prove that a straight <conditional mean> is inappropriate.
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