What Is a Good Model?
It is not difficult to quantify these deviations, as the differences Yi − μ(xi) are identical to the errors ei, and hence the standard deviation σe of the error term mea-
sures the average size of these deviations. And in Section 12.3 we have learned how we can estimate this standard deviation (also in the case of more than one covariate), and in the output of a regression, this estimate is often presented as the root mean squared error. Typically, this number is easy to interpret, as the standard deviation is expressed in the same units as the outcome Y , and we have just to remember that the interval μi(x)± 2σˆe covers Yi with a probability of 95%. For example, if Y are systolic blood pressure measurements, and we obtain an estimate for σe of 8.3, we know that Yi is on average rather close to μi, but if we obtain an estimate of 28.3, we would not longer say that the model is fitting the data well.