6.12 Next Up: Explaining Error

Let’s summarize where we are. We have developed the idea of the mean as a model. We have developed some statistics that quantify the amount of error around the model. And, we have shown that the mean is the point in the distribution of a quantitative variable where the squared deviations from the mean are at their lowest level.

We can think of the squared deviations from the mean of the distribution as the total amount of variation left after we take out the empty model (the model with just the mean). This is the unexplained variation, the error still left in our model, and it is as low as we can get it without adding an explanatory variable.

In the next section we will do just that. We will add an explanatory variable, and show how that changes our model and the amount of error left unexplained by our model. We will set out on a quest to reduce error, which is, after all, our goal.