Free Printable WorksheetMathAlgebra IMath CurriculumS-ID.5–9

ALG1.124 Residuals and Correlation for Model Fit Answer Key Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.124 Residuals and Correlation for Model Fit Answer Key. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.124 Residuals and Correlation for Model Fit - Identify residuals and correlation to judge how well a linear model fits data; Identify patterns or outliers that suggest a different model may be better. (CCSS: S-ID.5–9; TEKS: §111.39(b)(3) and technology use; VA SOL: A.ST.1 d–i; FL B.E.S.T.: MA.912.DP.1.1 (displays) with Algebra 1 modeling links (AR.2.5); NY-NGLS: AI-S.ID.5–9; CA CCSSM: S-ID.5–9; MA 2017: HS.S-ID.5–9; DoDEA CCRSM; NAEP: Algebra—modeling with data; NCTM P2A: Practices 4, 5.)

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Grade

Algebra I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related ALG1.124 Residuals and Correlation for Model Fit Answer Key skill assessments:

Problem 1Difficulty: Mastery
Use the display shown. A scatter plot has a strong upward trend with r = 0.93, but the matching residual plot rises from negative residuals at low x-values to positive residuals at high x-values. Which final judgment is best?
AThe fitted line is perfect because r is greater than 0.90.
BThe residual plot proves a negative correlation.
CThe data have strong positive association, but the fitted line's slope appears too small.
DThe data have no association because r is positive.
Solution & Explanation:The value r = 0.93 shows strong positive linear association. However, residuals increasing from negative to positive show a systematic error pattern, suggesting the line is not steep enough.
Problem 2Difficulty: Mastery
The model y = 0.8x + 12 is used for a data point with x = 25. The residual is -4. What is the actual y-value, and what does the sign mean?
A36; the model underpredicted by 4.
B32; the prediction was exact.
C28; the model overpredicted by 4.
D-4; the actual value equals the residual.
Solution & Explanation:The model predicts 0.8(25) + 12 = 32. Since residual = observed - predicted, observed = 32 - 4 = 28. A negative residual means the prediction was too high.
Problem 3Difficulty: Mastery
A data set has x-values between 10 and 50. A linear model has random residuals in that range. Which prediction is least supported by the residual evidence?
APredicting at x = 48
BPredicting at x = 20
CPredicting at x = 500
DPredicting at x = 35
Solution & Explanation:Residuals support the model only over the observed range, 10 to 50. A prediction at x = 500 is far outside that range and is an extrapolation.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard S-ID.5–9 (Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.5–9. Skill statement in this prompt cell: Identify residuals and correlation to judge how well a linear model fits data; Identify patterns or outliers that suggest a different model may be better. Associated standards listed with this skill in the curriculum source: CCSS: S-ID.5–9; TEKS: §111.39(b)(3) and technology use; VA SOL: A.ST.1 d–i; FL B.E.S.T.: MA.912.DP.1.1 (displays) with Algebra 1 modeling links (AR.2.5); NY-NGLS: AI-S.ID.5–9; CA CCSSM: S-ID.5–9; MA 2017: HS.S-ID.5–9; DoDEA CCRSM; NAEP: Algebra—modeling with data; NCTM P2A: Practices 4, 5. Use this prompt-provided wording as the supporting standard description for this workflow.).

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