What does a residual plot help determine in regression analysis?

A residual plot is a crucial tool in regression analysis as it helps assess the fit of the regression model. The residual plot displays the residuals on the vertical axis and the independent variable on the horizontal axis. Residuals are the differences between the observed values and the values predicted by the model. By examining the pattern of these residuals, analysts can determine if the model adequately captures the relationship between the variables.

If the residuals are randomly scattered around zero without any discernible pattern, this suggests that the model is a good fit for the data. Conversely, if the residuals display a systematic pattern (such as a curve), this indicates that the model may be mis-specified, potentially omitting important variables or using an inappropriate form of the model.

This analysis of residuals is distinct from determining correlation, coefficient significance, or overall dataset variability. While other analyses may provide insights into these areas, the residual plot specifically focuses on whether the regression model serves well to explain the relationship between the dependent and independent variables based on the data provided.