Math Problem Statement

Match the scatter plots with their respective residual plots and determine the suitability of the lines of best fit.

Solution

This image contains scatter plots with lines of best fit and corresponding residual plots. Let us analyze each plot and match the scatter plots to their residuals. Additionally, I will explain the reasoning for each match.

Analysis:

  1. Scatter Plot A:

    • The data shows a clear curve, indicating a non-linear relationship. The line of best fit here is a horizontal line, which is not appropriate for this data set.
    • The residual plot that matches this behavior is Residual Plot 2, as it shows a distinct pattern (parabolic shape), indicating the line does not capture the non-linear trend well.
  2. Scatter Plot B:

    • The data follows a perfectly linear trend, and the line of best fit accurately represents it.
    • The residual plot that matches this behavior is Residual Plot 3, as it shows no discernible pattern and minimal deviation from zero, indicating a good fit.
  3. Scatter Plot C:

    • The data is roughly linear, but the points deviate slightly from the line of best fit.
    • The residual plot that matches this behavior is Residual Plot 1, as it shows scattered residuals with no clear pattern, implying the linear model is adequate but not perfect.

Final Matches:

  • Scatter Plot AResidual Plot 2
  • Scatter Plot BResidual Plot 3
  • Scatter Plot CResidual Plot 1

Would you like more details or explanations?


Follow-up Questions:

  1. What does a residual plot with no pattern indicate about a model's fit?
  2. Why is it important to examine both the scatter plot and residual plot when assessing a model?
  3. How can a scatter plot help determine the suitability of a linear vs. non-linear model?
  4. What are some methods to improve the fit if the residuals show a pattern?
  5. How does the spread of points in a residual plot indicate the variance of errors?

Tip:

A residual plot with no clear pattern and small residuals generally indicates that the chosen model is a good fit for the data!

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Math Problem Analysis

Mathematical Concepts

Scatter plots
Residual plots
Lines of best fit

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12