The question is asking which residual plots indicate a good fit for linear regression. Here's how to interpret the given plots:

1. Residual Plot Analysis:
   • In linear regression, a good fit is indicated by a residual plot that shows no discernible pattern or trend (random scatter around zero).
   • The residuals should be distributed evenly across the range of the independent variable $x$, without any systematic pattern like curvature, clustering, or increasing/decreasing variance.

Examination of the Residual Plots:

• Plot I: The residuals are scattered randomly around the horizontal axis (zero residual line). This indicates a good fit for linear regression.
• Plot II: The residuals show a curved pattern, which suggests that a linear model is not appropriate. This indicates a bad fit.
• Plot III: The residuals appear to be zero for all values of $x$, which might occur in a perfectly deterministic linear relationship. This also indicates a good fit (though rarely happens in real data).

Answer:

Plots I and III indicate a good fit for a linear regression. Hence, the correct answer is (A) I and III only.

Do you need more details or have any other questions? Here are 5 related questions to deepen understanding:

1. Why is it important for residuals to show no pattern in a good linear regression fit?
2. What are some common patterns in residual plots that indicate problems with linear regression models?
3. How can non-linearity in residuals (like in Plot II) be addressed?
4. What role does homoscedasticity play in evaluating residual plots?
5. How can you visually or statistically assess residual normality?

Tip: Always check for randomness and equal spread of residuals across all $x$-values to evaluate the assumptions of linear regression.