Problem

Assess a linear functional form for residuals \({-1.1,0.8,-0.4,1.0,-0.3}\) in increasing-\(x\) order. Report the sign pattern, describe any systematic pattern, judge linear-form plausibility, and state the limitation caused by missing residual scale and context.

Source modeling plot: Assess only whether a linear functional form is appropriate. Residuals in increasing-x order are {-1.1,0.8,-0.4,1.0,-0.3}. No fitted model or assessment is annotated.

Big Picture

What this problem is really about

Residuals diagnose whether a model leaves a systematic shape unexplained. Read their signs in input order and look for sustained runs, curvature, or one-sided regions; scatter around zero supports the form, but without error units and context it does not establish practical predictive accuracy.

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signs=−,+,−,+,−; pattern=no monotone/curved run; assessment=linear form exact and highly accurate; limitation=residual scale/context is ignored

signs=−,+,−,+,−; pattern=residuals around0; assessment=linear form not appropriate because residuals mean misses; limitation=random scatter is treated as evidence against linearity

signs=−,+,−,+,−; pattern=residuals scatter around0 with nonzero values; assessment=linear form not appropriate because any residual is nonzero; limitation=residual scale/context is not considered

signs=-,+,-,+,-; pattern=no monotone/curved run and residuals scatter around0; assessment=linear form is plausible; limitation=residual scale/context is not supplied, so overall predictive accuracy cannot be judged

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Assess a linear functional form for residuals \({-1.1,0.8,-0.4,1.0,-0.3}\) in increasing-\(x\) order. Report the sign pattern, describe any systematic pattern, judge linear-form plausibility, and state the limitation caused by missing residual scale and context.

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