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

Examination of partial correlations.
Because of the problem just mentioned in
relying on zero-order correlations, Farrar and Glauber have suggested that one should look
at the partial correlation coefficients.
19
Thus, in the regression of 
Y
on 
X
2
, 
X
3
, and 
X
4
, a find-
ing that 
R
2
1
.
2 3 4
is very high but 
r
2
1 2
.
3 4
,
r
2
1 3
.
2 4
, and 
r
2
1 4
.
2 3
are comparatively low may suggest
that the variables 
X
2
, 
X
3
, and 
X
4
are highly intercorrelated and that at least one of these vari-
ables is superfluous.
Although a study of the partial correlations may be useful, there is no guarantee that
they will provide an infallible guide to multicollinearity, for it may happen that both 
R
2
and
all the partial correlations are sufficiently high. But more importantly, C. Robert Wichers
has shown
20
that the Farrar–Glauber partial correlation test is ineffective in that a given
partial correlation may be compatible with different multicollinearity patterns. The
R
2
4
.
2 3
=
r
2
4 2
+
r
2
4 3
−
2
r
4 2
r
4 3
r
2 3
1
−
r
2
2 3
338
Part Two
Relaxing the Assumptions of the Classical Model
19
D. E. Farrar and R. R. Glauber, “Multicollinearity in Regression Analysis: The Problem Revisited,”
Review of Economics and Statistics,
vol. 49, 1967, pp. 92–107.
20
“The Detection of Multicollinearity: A Comment,” 
Review of Economics and Statistics,
vol. 57, 1975,
pp. 365–366.
guj75772_ch10.qxd 12/08/2008 02:45 PM Page 338

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Chapter 10
Multicollinearity: What Happens If the Regressors Are Correlated?
339
Farrar–Glauber test has also been severely criticized by T. Krishna Kumar
21
and John
O’Hagan and Brendan McCabe.
22
4.