Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-IF.1-6,9

Pre CAL.28 Analyze Residuals and Model Fit Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.28 Analyze Residuals and Model Fit. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.28 Analyze Residuals and Model Fit - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given residual plots or residual summaries for two models, determine which model fits better and identify evidence of underfitting or overfitting. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

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 Pre CAL.28 Analyze Residuals and Model Fit skill assessments:

Problem 1Difficulty: Mastery
Model A has lower training error, but its residual plot is U-shaped and its validation RMSE is 6.2. Model B has higher training error, random residuals, and validation RMSE 2.9. Which evidence would justify selecting Model B?
AModel B's training error is higher
BModel B has lower validation error and no systematic residual pattern
CModel A's residual plot is U-shaped
DModel A has lower training error
Solution & Explanation:Model B is justified by the combination of better validation performance and a random residual plot. Model A shows underfitting despite lower training error.
Problem 2Difficulty: Mastery
For growth data, a logarithmic model has residuals positive early and negative late, while an exponential model has lower validation RMSE and random residuals. Which conclusion is best?
AUse the logarithmic model because it has a residual pattern
BUse the exponential model because both validation error and residual pattern are better
CUse neither because growth data cannot be modeled
DUse the logarithmic model because positive residuals are always good
Solution & Explanation:The logarithmic residual pattern shows systematic error. The exponential model has lower validation RMSE and random residuals, so it is better supported.
Problem 3Difficulty: Mastery
Model A has absolute validation residuals 1, 1, 2, 2, and 10. Model B has absolute validation residuals 3, 3, 3, 3, and 3. By how much is Model A's MAE lower than Model B's?
Solution & Explanation:Model A's MAE is 14/5 = 2.8. Model B's MAE is 15/5 = 3.0. Model A is lower by 0.2.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSF-IF.1-6,9 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-IF.1-6,9. Skill statement in this prompt cell: Given residual plots or residual summaries for two models, determine which model fits better and identify evidence of underfitting or overfitting. Associated standards listed with this skill in this prompt cell: CCSS HSF-IF.1-6,9; CCSS HSF-BF.1-4; CCSS HSA-CED.1-4; SMP 1,2,4,5,7; AP Precalculus CED Units 1-3; TX §111.42(c)(2)(A-L); FL MA.912.F.1.4, MA.912.F.1.7, MA.912.F.3.3-3.9, MA.912.AR.9.10; VA MA.CF.1, MA.FR.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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