Based on the residual plot, which of the following indicates that a linear regression model is appropriate for the data?

• A. The residuals increase or decrease systematically as the fitted values increase.
• B. The residuals are randomly scattered around $0$ with no apparent pattern.
• C. The residuals show a clear curved pattern.
• D. The residuals form a funnel shape, with increasing spread as fitted values increase.

Answer: (B)

Verified step by step guidance

1. Understand that a residual plot displays the residuals (differences between observed and predicted values) on the vertical axis and the fitted values on the horizontal axis.
2. Recall that for a linear regression model to be appropriate, the residuals should not show any systematic pattern when plotted against the fitted values.
3. Identify that if residuals increase or decrease systematically, it suggests a non-linear relationship, indicating the linear model may not be suitable.
4. Recognize that a clear curved pattern in residuals also indicates non-linearity, meaning the linear model does not fit well.
5. Note that residuals forming a funnel shape (heteroscedasticity) suggest non-constant variance, violating linear regression assumptions, so the residuals should be randomly scattered around zero with no apparent pattern for the model to be appropriate.