In residuals analysis, what should the residual plot look like if the regression line fits the data well?

• A. The residuals should show a distinct curve or systematic pattern.
• B. The residuals should form a clear upward or downward trend.
• C. The residuals should be randomly scattered around the horizontal axis with no clear pattern.
• D. The residuals should all be close to zero on one side of the axis.

Answer: (C)

Verified step by step guidance

1. Understand that residuals are the differences between observed values and the values predicted by the regression line, calculated as \(\text{residual} = y_{observed} - y_{predicted}\).
2. Recognize that a good regression fit means the model captures the underlying relationship well, so residuals should not show any systematic pattern.
3. Interpret the residual plot: if the regression line fits well, residuals should be randomly scattered around the horizontal axis (which represents zero residual), indicating no bias in predictions.
4. Note that if residuals show a curve, trend, or pattern, it suggests the model is missing some structure in the data, indicating a poor fit.
5. Therefore, the key characteristic of a residual plot for a well-fitting regression line is randomness and no clear pattern, with residuals evenly distributed above and below zero.