Free Printable WorksheetMathPre-CalculusMath CurriculumS-ID.6

Pre CAL.164 Residuals and Goodness of 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.164 Residuals and Goodness of Fit. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.164 Residuals and Goodness of Fit - Primary standard selected for prompt fields in this prompt cell: CCSS S-ID.6. Skill statement in this prompt cell: Given a residual plot or summary, determine whether the model is appropriate and select the interpretation that correctly uses residual evidence. 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.164 Residuals and Goodness of Fit skill assessments:

Problem 1Difficulty: Mastery
Three models are tested. Model 1 has random residuals but RMSE 12. Model 2 has RMSE 5 with a strong U-shaped residual plot. Model 3 has RMSE 6 with residuals randomly scattered and no extreme outliers. Which model is the best candidate?
AModel 1, because random residuals always matter more than error size.
BModel 2, because the lowest RMSE always overrides a strong residual pattern.
CNo model can be compared unless all residuals are positive.
DModel 3, because it has low typical error and no clear residual pattern.
Solution & Explanation:Model 3 has a good combination of reasonably low RMSE and random residuals. Model 2's lower RMSE is weakened by the U-shaped pattern.
Problem 2Difficulty: Mastery
A final report compares a linear model and a quadratic model. The linear model has a curved residual plot and RMSE 6.5. The quadratic model has random residuals and RMSE 3.8. Which report sentence is best?
AThe linear model is more appropriate because curved residuals prove linearity.
BBoth models are equally good because neither has RMSE equal to 0.
CThe quadratic model is more appropriate because its residuals show no clear pattern and its typical error is smaller.
DThe model with the longer equation should always be selected.
Solution & Explanation:The quadratic model improves both residual pattern and typical error, so residual evidence and RMSE both support it over the line.
Problem 3Difficulty: Mastery
A residual is -8 and the model's RMSE is 4. What is the residual measured in RMSE units?
Solution & Explanation:Divide the residual by the RMSE: -8 / 4 = -2. The point is 2 RMSE units below the prediction.

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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 a residual plot or summary, determine whether the model is appropriate and select the interpretation that correctly uses residual evidence. 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.).

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