What might a non-random pattern in a residuals plot suggest?

A non-random pattern in a residuals plot suggests that the model used to fit the data may be inappropriate. In a well-fitted regression model, the residuals—which are the differences between the observed values and the values predicted by the model—should display a random pattern when plotted against predicted values or against the independent variable. A random pattern indicates that the model has captured the underlying relationship well, and any randomness in the data is expected.

However, if there is a discernible pattern in the residuals (such as a curve or clustering), it can indicate that the model is not adequately explaining the data. This might mean that the model is missing key variables, has the wrong functional form, or may require transformation of the variables to better fit the data. Thus, recognizing a non-random pattern in residuals is critical for diagnosing and improving the model's performance.