Problem

Apply the stated pattern-first model rule to \(A\) residuals \({-3,2,-1,3,-2,1}\), random in \(x\)-order, and \(B\) residuals \({-1,-0.2,0.8,0.8,-0.2,-1}\), forming a curve. Which complete response correctly applies the model-comparison rule?

Source residual-model comparison: Priority rule: reject a model with a clear systematic residual pattern when the other has random scatter; otherwise choose smaller MAE, then smaller |mean residual| as tie-breaker. A residuals={−3,2,−1,3,−2,1} are random in x-order; B={−1,−0.2,0.8,0.8,−0.2,−1} form a curved pattern. Which model should be selected under this rule? No MAE, mean residual, or model choice is annotated.

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A pattern=random, MAE=12/6=2; B pattern=systematic curved, MAE=4/6≈0.667; choice=A by pattern priority despite larger MAE

A pattern=random, MAE=2, mean=0; B pattern=systematic curved, MAE≈0.667, mean≈−0.133; priority=farther residuals are treated as capturing variation; choice=A

A pattern=random, MAE=2, mean=0; B pattern=systematic curved, MAE≈0.667, mean≈−0.133; priority=smaller MAE is treated as always winning; choice=B

A pattern=random, MAE=2, mean=0; B pattern=systematic curved, MAE≈0.667, mean≈−0.133; priority=organized curve is treated as good evidence; choice=B

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Apply the stated pattern-first model rule to \(A\) residuals \({-3,2,-1,3,-2,1}\), random in \(x\)-order, and \(B\) residuals \({-1,-0.2,0.8,0.8,-0.2,-1}\), forming a curve. Which complete response correctly applies the model-comparison rule?

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