Residuals

Residuals are the error, or difference, between the model and the observed data. The residual vector $\bold R = \{r_1, \ldots,r_n\}$ is defined by

$$r_i = d_i - \bold{N} (t, \bold P) .$$

The residual vector is plotted in Figure 5B.

We can also calculate residuals as percentage error:

$$r_i = \frac{(d_i - \bold{N} (t, \bold p))} {\bold N(t, \bold p)} \times 100.$$

It is crucial to examine the residuals after a fit. When a fit is ``good,'' the residuals are non-uniformly distributed around the zero axis; that is, they appear to be random in magnitude and sign. A substantial or systematic deviation from the zero axis indicates some phenomenon is not being modeled or fitted correctly. An iterative process of fitting loglets to a data set and then examining the residuals is a good way to proceed, unless the errors in the data and shown in the residuals are known to come from other sources (e.g., a recession).

Loglet Lab provides views of both percentage and raw error.