Free Printable WorksheetMathPre-CalculusMath CurriculumS-ID.6

Pre CAL.163 Regression and Model Selection 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.163 Regression and Model Selection. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.163 Regression and Model Selection - Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Given data and regression outputs, determine which model best fits and select evidence (such as residuals or context constraints) that supports the choice. 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.163 Regression and Model Selection skill assessments:

Problem 1Difficulty: Mastery

When model choices are close, residual plots and context constraints are valid evidence for deciding which regression model is most appropriate.

ATrue, both are valid evidence in regression model selection

BFalse, only the largest coefficient matters

CFalse, context constraints should be ignored

DTrue, but only when every residual is zero

Solution & Explanation:Regression model selection is not based on one statistic alone. Residual behavior and context constraints are essential evidence.

Problem 2Difficulty: Mastery

A factory's output increases by about the same number of units each month. A linear model has random residuals and validation RMSE 4.2. An exponential model has slightly higher training R-squared but validation RMSE 9.1. Which model should be chosen?

ALinear, because the context suggests constant rate and validation error is lower

BExponential, because training R-squared is slightly higher

CQuadratic, because all output data curve

DLogistic, because output must have an upper bound in every question

Solution & Explanation:The linear model matches the constant-rate context, has random residuals, and predicts better on validation data.

Problem 3Difficulty: Mastery

Twelve monthly sales values repeat a seasonal pattern. A degree-11 polynomial fits the 12 training points exactly, but a sinusoidal model has much lower validation error on the next 12 months. Which model is better?

ADegree-11 polynomial, because it has zero training residuals

BSinusoidal, because the context is seasonal and validation error is lower

CLinear, because months are numeric

DExponential, because sales can grow

Solution & Explanation:Seasonal data repeat. The sinusoidal model matches the context and performs better on validation data, so it is better supported.

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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 S-ID.6 (Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Given data and regression outputs, determine which model best fits and select evidence (such as residuals or context constraints) that supports the choice. 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.).