  In various economic applications, people want to compare $n$ units with
respect to certain quantities $Y_1, Y_2, \ldots, Y_n$ measuring their
performance. The latter, however, is often influenced by certain factors which
are beyond control of the units, and one would like to extract an adjusted
performance from the data. Specifically, let $X_i \in \mathcal{X}$ summarize
the factors of the $i$-th unit. Then one could think of a model equation $Y_i =
f_o(X_i) + \epsilon_i$ with a regression function $f_o : \mathcal{X} \to
\mathbb{R}$ describing the unavoidable influence of the factors $X_i$ and
$\epsilon_i$ being the adjusted performance of the $i$-th unit. Now a common
proposal is to estimate $f_o$ via regression methods by a function $\hat{f}$
depending on the current data $(X_i,Y_i)$, possibly augmented by additional
past data, and to use the residuals $\hat{\epsilon}_i := Y_i - \hat{f}(X_i)$ as
surrogates for the adjusted performances $\epsilon_i$. In the present report we
discuss this approach, its potential pitfalls and (mis)interpretation. In
particular, an unavoidable property of the residuals $\hat{\epsilon}_i$ is that
they measure only parts of the adjusted performance while the remaining parts
get hidden in the estimated function $\hat{f}$. Possible alternatives are
mentioned briefly.
