What is the primary utility of a residuals plot in regression analysis?

A residuals plot is primarily used to assess the appropriateness of a regression model. When plotting residuals, which are the differences between the observed values and the predicted values, you can visually inspect whether the residuals display any systematic patterns. If the plot shows a random scatter of points around the horizontal axis (zero line), it suggests that the regression model is a good fit for the data, meaning that the linearity assumption holds true. On the other hand, patterns such as curves or clusters in the residuals can indicate that the model may not be adequate, possibly suggesting that a different model (such as a non-linear model) might be more appropriate. This function of assessing model fit is critical in determining how well the regression analysis has captured the underlying relationship between the variables.

The other responses touch on important aspects of statistical analysis but do not directly connect to the primary utility of a residuals plot in the context of evaluating model fit. For instance, while a residuals plot indirectly supports understanding the relationship between variables, it does not show that relationship directly. Similarly, calculating the correlation coefficient is a separate task that quantifies the strength of the linear relationship but does not evaluate model fit. Lastly, the mean of residuals is generally expected to be