The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

The “Incremental” or “Marginal” Contribution
of an Explanatory Variable
In Chapter 7 we stated that generally we cannot allocate the 
R
2
value among the various re-
gressors. In our child mortality example we found that the 
R
2
was 0.7077 but we cannot say
what part of this value is due to the regressor PGNP and what part is due to female literacy
rate (FLR) because of possible correlation between the two regressors in the sample at
hand. We can shed more light on this using the analysis of variance technique.
For our illustrative example we found that 
individually X
2
(PGNP) and 
X
3
(FLR) were
statistically significant on the basis of (
separate
)
t
tests. We have also found that on the
basis of the 
F 
test
collectively
both the regressors have a significant effect on the regressand
Y
(child mortality).
Now suppose we introduce PGNP and FLR
sequentially;
that is, we first regress child
mortality on PGNP and assess its significance and then add FLR to the model to find out
whether it contributes anything (of course, the order in which PGNP and FLR enter can be re-
versed). By contribution we mean whether the addition of the variable to the model increases
ESS (and hence
R
2
) “significantly” in relation to the RSS. This contribution may appropri-
ately be called the
incremental,
or
marginal,
contribution of an explanatory variable.
The topic of incremental contribution is an important one in practice. In most empirical
investigations the researcher may not be completely sure whether it is worth adding an 
X
variable to the model knowing that several other 
X
variables are already present in the
model. One does not wish to include a variable(s) that contributes very little toward ESS.
By the same token, one does not want to exclude a variable(s) that substantially increases
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