Thinking and Deciding

364 QUANTITATIVE JUDGMENT
procedure may involve many of the same processes as evaluation, so we discuss it
here too.
A major question in the study of judgment concerns the relative efficacy of unaided
holistic judgment — in which the judge simply assigns a number to each case
— and judgment aided by the use of calculations, like those done in MAUT. The answers
to this question have strong implications for decision making in government,
business, and the professions, and in any situation where important decisions are
made about a number of cases described on the same dimensions.
Multiple linear regression
Most of the literature on judgment has looked at situations in which each of a number
of possibilities, such as applicants for college, is characterized by several numbers.
Each number represents a value on some dimension, or cue, such as grades or quality
of recommendations. The judge’s task is to evaluate each possibility with respect to
some goal (or goals), such as college grades as a criterion of success in college. Each
dimension or cue has a high and low end with respect to the goal. For example, high
test scores are assumed to be better than low test scores. In these situations a certain
kind of normative model is assumed to apply, specifically, a statistical model called
multiple linear regression (or just regression, for short). 1
Let us take an extremely simple, somewhat silly, example of predicting a student’s
final-exam grade (F) from the grades on a paper (P) and a midterm exam
(M). Table 15.1 shows the three grades. A computer finds a formula that comes
as close as possible to predicting F from M and P. In this case, the formula is
F = .71 · M + .33 · P − 2.3. The predicted values, computed from the formula, are
in the column labeled PRE. You can see that the predictions are not perfect. The last
column shows the errors.
The usual method of regression, illustrated here, chooses the formula so that the
prediction is a linear sum of the predictors, each multiplied by a weight, and the
sum of the squares of the errors is minimized. The formula also contains a constant
term, in this case −2.3, which makes sure that the mean of the predicted values is
the same as the mean of the real ones. The weights are roughly analogous to weights
in MAUT (p. 341).
The same method is useful in many other situations in which we want to predict
one variable from several others, and in which we can expect this sort of linear formula
to be approximately true. That is, we should expect the dependent variable —
F in this case — to increase (or decrease) with each of the predictors. Examples are:
predicting college grades from high-school grades and admissions tests (Baron and
Norman, 1992); election margins from economic data (Fair, 2002); and wine quality
from weather data in the year the grapes were grown (Fair, 2002; see Armstrong,
2001, for other examples).
1 Economists call it “ordinary least squares” regression, or OLS, because the method involves minimizing
the sum of the squared errors of prediction.