When modeling data one important rule to consider states: the model should fit the data and not vice versa. There is one problem well known by teachers and researchers: Students often do not realize the gap between data and model, they mistakenly consider the model as reality. In this situation the residuals defined as the difference between data and model become important: they remind us of modeling the trend in data and not the data itself. Whereas the model stands for the explained variation, the residuals represent the unexplained variation. This is at the core of statistical thinking. In this paper, the significance of the residuals for modeling data is examined from different perspectives.