To solve this question, we have to understand what residuals actually represent in the context of statistical modelling.
Residuals essentially stand for the difference between the actual values, i.e., the observed data, and the values predicted by the mathematical model being used. This could be any kind of statistical model - simple, complex, linear, non-linear, etc.
So let's now go through the options:
A) The claim that values of residuals from an empty model will equal those from a complex model is neither guaranteed nor universally true. The magnitude and direction of residuals depend directly on how well the model, complex or simple, predicts the data.
B) This statement is true. As mentioned earlier, residuals represent differences between data and a model's prediction. So, irrespective of whether the model is simple or complex, this definition holds.
C) This statement is incorrect. Residuals do not typically denote differences between the data and the Grand Mean. The Grand Mean is the mean of all the data collectively, not individual values.
D) Lastly, this option is also not true all the time. Even with the most meticulous data entry and measurement, there can still be residuals. The presence of residuals does not necessarily indicate a mistake in data recording, but rather the degree to which the model fits the given data.
So, going through all the options, the correct answer would be B: The residuals represent the difference between the data and the model's prediction.