Problem

Specify the residual plot for inputs \(1,~2,~3,~4\) and residuals \(-1,~2,~0,~-2\), using \(x~\text{from}~1~\text{to}~4~by~1\), \(\text{residual}~y~\text{from}~-2~\text{to}~2~by~1\), and a horizontal \(\text{zero}\) line. Give the points, count, above/on/below totals, and pattern note.

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What this problem is really about

A residual plot uses the original input horizontally and its paired residual vertically. Plot every ordered pair without swapping or negating coordinates, draw the zero reference line, and count points above, on, and below it before describing any ordered pattern.

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points=(1,1),(2,2),(3,3),(4,4); count=4; zero line y=0; above=4,on=0,below=0; pattern note=inputs are incorrectly plotted as residual y-values

points=(-1,1),(2,2),(0,3),(-2,4); count=4; zero line y=0; above=2,on=1,below=1; pattern note=coordinate pairs are swapped

points=(1,1),(2,-2),(3,0),(4,2); count=4; zero line y=0; above=2,on=1,below=1; pattern note=every residual sign is negated

points=(1,-1),(2,2),(3,0),(4,-2); count=4; zero line y=0; above=1,on=1,below=2; pattern note=no monotone all-one-side run is established from these four points

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Specify the residual plot for inputs \(1,~2,~3,~4\) and residuals \(-1,~2,~0,~-2\), using \(x~\text{from}~1~\text{to}~4~by~1\), \(\text{residual}~y~\text{from}~-2~\text{to}~2~by~1\), and a horizontal \(\text{zero}\) line. Give the points, count, above/on/below totals, and pattern note.

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