Residual Plots Worksheet
A Grade 10 Math worksheet on interpreting and creating residual plots to assess the fit of a linear model.
Includes
Standards
Topics
Residual Plots: Assessing Linear Models
Name:
Date:
Score:
Carefully read each question and provide your best answer. For questions involving graphs, pay close attention to the patterns in the residual plots to determine the appropriateness of a linear model.
1. What does a residual plot help us determine?
The strength of the linear correlation.
Whether a linear model is appropriate for the data.
The value of the y-intercept.
The slope of the regression line.
2. A good residual plot should show:
A clear parabolic pattern.
Residuals increasing as x increases.
No discernible pattern, scattered randomly around zero.
A funnel shape.
1. If a residual plot shows a clear curve, it suggests that a linear model is a good fit for the data.
True
False
2. Residuals are the differences between the observed y-values and the predicted y-values.
True
False
1. A residual plot graphs the against the .
2. If a residual plot shows a fanning out or fanning in pattern, it indicates .
1. Describe the ideal pattern for a residual plot when a linear model is appropriate.
2. You are given a scatter plot and its corresponding residual plot. The residual plot shows a distinct U-shape pattern. What does this tell you about the appropriateness of a linear model for the original data?
Examine the following residual plots and determine if a linear model is appropriate for the data in each case. Justify your answer.
Residual Plot A:
Appropriate for linear model?
Justification:
Residual Plot B:
Appropriate for linear model?
Justification:
1. A scientist collected data on the growth of a plant over several weeks. She then performed a linear regression and generated a residual plot. The residual plot showed that for smaller predicted values, the residuals were mostly positive, and for larger predicted values, the residuals were mostly negative, forming a curved pattern. Explain what this pattern suggests about the relationship between plant growth and time, and what the scientist should consider next.