Free Printable WorksheetMathPre-CalculusMath CurriculumHSF-LE.1-5

Pre CAL.73 Use Residuals to Compare Competing Models 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.73 Use Residuals to Compare Competing Models. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.73 Use Residuals to Compare Competing Models - Primary standard selected for prompt fields in this prompt cell: CCSS HSF-LE.1-5. Skill statement in this prompt cell: Given residual plots or statistics for two models, determine which model is better supported and select the evidence that justifies that selection. Associated standards listed with this skill in this prompt cell: CCSS HSF-LE.1-5; CCSS HSF-BF.3-5(+); CCSS HSA-REI.11; SMP 1,2,4,5,7; AP Precalculus CED Unit 2; TX §111.42(c)(5)(J-M); FL MA.912.AR.5; VA MA.FR.2. 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

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.73 Use Residuals to Compare Competing Models skill assessments:

Problem 1Difficulty: Mastery

A teacher asks which model is better supported by residual evidence. Model A has lower RMSE, but its residuals show a funnel and a curved trend. Model B has slightly higher RMSE, constant spread, and no trend. Which answer is best?

AModel A; lower RMSE is the only criterion

BModel B; residual randomness and constant spread outweigh a slight RMSE disadvantage

CModel A; funnel plus curve is ideal

DModel B; higher RMSE is always better

Solution & Explanation:Model A has two residual-pattern warnings. Model B's residuals are more appropriate even with a slightly higher RMSE.

Problem 2Difficulty: Mastery

Two models are fit to the same exponential-growth data. Model A residuals on the original scale are small at early x-values but large and positive at late x-values. Model B residuals are slightly larger early but balanced at late x-values. The purpose is predicting late growth. Which model is better supported?

AModel A; early small residuals are the only relevant evidence

BModel B; late-x residuals are more balanced for the prediction purpose

CModel A; positive late residuals prove late predictions are exact

DModel B; early residuals should never be considered

Solution & Explanation:The purpose focuses on late growth, so late-x residual behavior matters. Model B is less biased in that region.

Problem 3Difficulty: Mastery

A model comparison report says Model A residuals are smaller after deleting three inconvenient data points. Model B residuals are slightly larger but are computed on the complete data set. No reason is given for deleting points. Which conclusion is best?

AModel A is better because smaller residuals after deletion always win

BModel B is better supported unless the deletions are justified, because the comparison must use the same valid data

CModel A is better because fewer data points make any model more accurate

DNeither model can ever use residuals if a point is deleted

Solution & Explanation:Residual evidence is trustworthy only when models are compared on the same valid data or exclusions are justified. Unexplained deletion weakens Model A's evidence.

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Frequently Asked Questions

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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-LE.1-5 (Primary standard selected for prompt fields in this prompt cell: CCSS HSF-LE.1-5. Skill statement in this prompt cell: Given residual plots or statistics for two models, determine which model is better supported and select the evidence that justifies that selection. Associated standards listed with this skill in this prompt cell: CCSS HSF-LE.1-5; CCSS HSF-BF.3-5(+); CCSS HSA-REI.11; SMP 1,2,4,5,7; AP Precalculus CED Unit 2; TX §111.42(c)(5)(J-M); FL MA.912.AR.5; VA MA.FR.2. Use this prompt-provided wording as the supporting standard description for this workflow.).