Residual Plots Worksheet

Residual Plots: Assessing Linear Models

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?

2. A good residual plot should show:

1. If a residual plot shows a clear curve, it suggests that a linear model is a good fit for the data.

2. Residuals are the differences between the observed y-values and the predicted y-values.

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.