Which residual plot indicates that the model is a good fit for the data?

• A. A plot where the $residuals$ are randomly scattered around the horizontal axis with no apparent pattern
• B. A plot where the $residuals$ form a clear $U$-shaped pattern
• C. A plot where the $residuals$ show a funnel shape, with increasing spread as fitted values increase
• D. A plot where the $residuals$ increase or decrease systematically as the fitted values increase

Answer: (A)

Verified step by step guidance

1. Understand that residuals are the differences between observed values and the values predicted by a regression model, calculated as \(\text{residual} = \text{observed} - \text{predicted}\).
2. Recognize that a good model fit is indicated when residuals show no systematic pattern, meaning they are randomly scattered around the horizontal axis (residual = 0 line). This randomness suggests the model captures the relationship well.
3. Identify that patterns such as a U-shape in the residual plot indicate the model is missing a nonlinear relationship, suggesting poor fit.
4. Note that a funnel shape (increasing spread of residuals) indicates heteroscedasticity, meaning the variance of errors is not constant, which violates regression assumptions.
5. Understand that residuals increasing or decreasing systematically with fitted values indicate a trend not captured by the model, signaling a poor fit.