In this question, we are asked to determine which residual plot (A, B, or C) indicates a good fit for a linear model. To evaluate this, we need to consider the pattern of residuals:

1. Residuals and Good Fit: For a linear model to be a good fit, the residuals should ideally be randomly scattered around the horizontal axis (zero residual line) without any clear pattern or structure. This randomness indicates that the model has captured all the relevant patterns in the data, and no systematic errors remain.

2. Assessing Each Plot:

   • Plot A: The residuals form a U-shaped pattern, which suggests a systematic curvature. This pattern indicates that a linear model might not be appropriate, as it fails to capture some curvature in the data. A non-linear model may be a better fit.
   • Plot B: The residuals are scattered randomly around the horizontal axis, with no apparent pattern or curvature. This suggests that a linear model might be suitable, as there is no systematic structure left unexplained.
   • Plot C: The residuals show an inverted U-shaped pattern, which, like Plot A, indicates a systematic trend that a linear model fails to capture. This implies that a non-linear model might be more appropriate.

3. Conclusion: Plot B is the one that indicates a good fit for a linear model, as the residuals are randomly dispersed around the horizontal axis without any clear pattern.

Would you like further details on residual analysis or have any additional questions?

Here are five related questions to deepen understanding:

1. What does a residual plot with a funnel shape suggest about the model fit?
2. How can residuals indicate the presence of heteroscedasticity in a model?
3. What role do outliers play in residual plots, and how can they affect model fit?
4. Why is randomness in residuals important for validating a linear model?
5. How would a residual plot look if the data were overfitted with too complex a model?

Tip: Residual plots are a powerful diagnostic tool; always check them to assess whether a linear model is appropriate for the data.