Given a residual plot that shows a random scatter of points around the horizontal axis with no apparent pattern, which conclusion is most appropriate about the use of a linear model?

• A. A linear model is not appropriate because the residuals increase in spread as the fitted values increase.
• B. A linear model is appropriate because the residuals show no clear pattern.
• C. A linear model is not appropriate because the residuals are all $+$.
• D. A linear model is not appropriate because the residuals show a curved pattern.

Answer: (B)

Verified step by step guidance

1. Understand what a residual plot represents: it shows 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 model to be appropriate, the residuals should be randomly scattered around the horizontal axis (residual = 0) without any systematic pattern.
3. Identify key patterns that indicate problems with a linear model: increasing spread of residuals (heteroscedasticity), all residuals being positive or negative (indicating bias), or a curved pattern (indicating non-linearity).
4. Analyze the given residual plot description: it shows a random scatter of points around the horizontal axis with no apparent pattern, which suggests the assumptions of linear regression are met.
5. Conclude that since the residuals show no clear pattern and are randomly scattered, the linear model is appropriate for the data.