Problem

Assess a linear functional form for residuals \({3,-1,-3,-1,3}\) in increasing-\(x\) order with upward-curving data. Describe the residual pattern, judge the linear form, propose the appropriate alternative shape, and state the evidence.

Source modeling plot: Assess a linear functional form from residuals {3,-1,-3,-1,3} in increasing-x order and upward-curving data. No fitted model or assessment is annotated.

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pattern=positive at both ends and negative in middle (U-shape); assessment=nonlinear because residuals are not zero; alternative=unspecified nonlinear model; evidence=any nonzero residual is treated as curvature

pattern=positive at both ends and negative in middle (U-shape); assessment=linear because U balances above/below; alternative=linear model; evidence=sign balance is treated as random scatter

pattern=positive at both ends and negative in middle (U-shape); assessment=linear form not appropriate; alternative=upward-curving nonlinear model; evidence=systematic residual curvature rather than random scatter

pattern=positive at both ends and negative in middle (U-shape); assessment=linear because data increase; alternative=linear model; evidence=overall increase is treated as sufficient

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Assess a linear functional form for residuals \({3,-1,-3,-1,3}\) in increasing-\(x\) order with upward-curving data. Describe the residual pattern, judge the linear form, propose the appropriate alternative shape, and state the evidence.

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