Free Printable WorksheetMathPre-CalculusMath CurriculumS-ID.6

Pre CAL.172 Use Technology to Create Residual Plots and Compare 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.172 Use Technology to Create Residual Plots and Compare Models. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.172 Use Technology to Create Residual Plots and Compare Models - Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Given technology-generated residual plots for two models, determine which model is better supported and select evidence from the plots. Associated standards listed with this skill in this prompt cell: CCSS S-ID.6; CCSS S-CP.1-6; CCSS HS-Modeling; SMP 1,2,4,5,6; VA A2.ST.3, PS.1; NAEP Data Analysis and Probability. 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.172 Use Technology to Create Residual Plots and Compare Models skill assessments:

Problem 1Difficulty: Mastery

Two models were fit for solar panel output versus sun angle, and technology produced the residual plots shown. Which decision is supported by the residual plots?

AChoose Model B; the visible pattern in its residuals is useful evidence that the model discovered structure.

BChoose the model with the largest single positive residual because it shows the model can handle extremes.

CThe two models cannot be compared unless the original scatterplot is shown instead of residual plots.

DChoose Model A (quadratic); it has no angle-related curved residual structure, while Model B (linear) shows a negative-positive-negative pattern by sun angle.

Solution & Explanation:A residual plot supports a model when the residuals are centered near 0 with no systematic pattern. Model A is better supported because it has no angle-related curved residual structure; Model B is weaker because it shows a negative-positive-negative pattern by sun angle.

Problem 2Difficulty: Mastery

Technology generated residual plots for two models of athletic jump height versus training weeks. Model A (linear) residual plot: residuals are positive for the first weeks and negative for later weeks. Model B (logarithmic) residual plot: residuals randomly scatter around 0 for early and later weeks. Which conclusion is best supported?

AChoose Model A; the visible pattern in its residuals is useful evidence that the model discovered structure.

BChoose the model with the largest single positive residual because it shows the model can handle extremes.

CChoose Model B (logarithmic); it removes the early-versus-late residual bias, while Model A (linear) has residual signs separated by training phase.

DThe two models cannot be compared unless the original scatterplot is shown instead of residual plots.

Solution & Explanation:A residual plot supports a model when the residuals are centered near 0 with no systematic pattern. Model B is better supported because it removes the early-versus-late residual bias; Model A is weaker because it has residual signs separated by training phase.

Problem 3Difficulty: Mastery

For download time versus file size, a student compares the two technology-generated residual plots shown. Which conclusion uses residual plot evidence correctly?

AChoose Model B; the more complicated model must be better even when the residual evidence is nearly unchanged.

BChoose Model A (linear); the residual plots and spreads are almost identical, so the simpler linear model is adequate, while Model B (quadratic) adds complexity for a negligible residual-spread change.

CChoose the model with the most residuals above 0 because positive residuals indicate accurate predictions.

DThe residual plots show the models are perfect because the residuals are centered near 0.

Solution & Explanation:A residual plot supports a model when the residuals are centered near 0 with no systematic pattern. Model A is better supported because the residual plots and spreads are almost identical, so the simpler linear model is adequate; Model B is weaker because it adds complexity for a negligible residual-spread change.

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Frequently Asked Questions

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QHow do I download and print this Pre CAL.172 Use Technology to Create Residual Plots and Compare Models worksheet?

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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 S-ID.6 (Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Given technology-generated residual plots for two models, determine which model is better supported and select evidence from the plots. Associated standards listed with this skill in this prompt cell: CCSS S-ID.6; CCSS S-CP.1-6; CCSS HS-Modeling; SMP 1,2,4,5,6; VA A2.ST.3, PS.1; NAEP Data Analysis and Probability. Use this prompt-provided wording as the supporting standard description for this workflow.).