Problem preview
S-ID.6.b Warmup M1-055-A08-V01

Assess model fit informally using residuals.

Compare models using residual summaries

Problem

Apply this model-comparison rule: reject a clear systematic residual pattern when the other model has random scatter; otherwise use smaller \(MAE\), then smaller \(|\text{mean}~\text{residual}|\). For \(A={-1,0,1,-1}\) and \(B={-5,3,4,-2}\), with neither pattern declared systematic, which complete response correctly applies the model-comparison rule?

Big Picture

What this problem is really about

Compare residual models with the stated priorities rather than one convenient statistic. Address systematic pattern first, then use mean absolute error for typical miss size; a signed mean near zero can result from positive and negative errors canceling, so it cannot replace the magnitude comparison.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
S-ID.6.b
Category
Statistics and Probability
Domain
Interpreting Categorical and Quantitative Data
Objective
Assess model fit informally using residuals.
Problem type
Compare models using residual summaries