Question

which residual plot shows that the model is a good fit for the data?

Explanation:

To determine which residual plot shows a good fit for the data, we analyze the distribution of residuals (the vertical distances between data points and the regression line):

Key Concept:

A good linear fit has residuals that are randomly scattered around the horizontal line (residual = 0) with no obvious pattern (e.g., curved, increasing/decreasing trend, or clustering).

Analyzing Each Plot:

1. First Plot: Residuals show a clear downward trend (curved or decreasing pattern) → Not a good fit.
2. Second Plot: Residuals form a U - shaped (curved) pattern → Not a good fit (indicates non - linearity).
3. Third Plot: Residuals are randomly scattered above and below the horizontal line with no consistent trend or pattern → This indicates the model (e.g., linear regression) fits the data well.

Answer:

The third residual plot (with randomly scattered residuals) shows that the model is a good fit for the data.