"Residual" in statistics refers to the difference between the calculated value of the dependent variable against a predicted value. The mean and the sum of the residuals are always equal to zero, and the value is positive if the data point is above the graph and negative if below it.
Checking for residual consistency is essential in validating any regression model. This is because unpredictability and randomness are critical components of it. The validation entails examining whether or not generated random error is consistent with the residuals points. From this observation, if the residuals show that the model is systematically incorrect, then the model should be improved.