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

Klein’ rule of thumb,
which suggests that multicollinearity may be a troublesome problem only if the 
R
2
obtained
from an auxiliary regression is greater than the overall 
R
2
, that is, that obtained from the
regression of 
Y
on all the regressors.
25
Of course, like all other rules of thumb, this one
should be used judiciously.
5.
Eigenvalues and condition index.
From 
EViews
and 
Stata
, we can find the 
eigen-
values
and the
condition index,
to diagnose multicollinearity. We will not discuss eigenvalues
here, for that would take us into topics in matrix algebra that are beyond the scope of this
F
i
=
R
2
x
i
·
x
2
x
3
···
x
k
(
k
−
2)
1
−
R
2
x
i
·
x
2
x
3
···
x
k
(
n
−
k
+
1)
21
“Multicollinearity in Regression Analysis,”
Review of Economics and Statistics,
vol. 57, 1975, pp. 366–368.
22
“Tests for the Severity of Multicollinearity in Regression Analysis: A Comment,” 
Review of Economics
and Statistics,
vol. 57, 1975, pp. 368–370.
23
For example, 
R
2
x
2
can be obtained by regressing 
X
2
i
as follows: 
X
2
i
=
a
1
+
a
3
X
3
i
+
a
4
X
4
i
+
· · · +
a
k
X
ki
+ ˆ
u
i
.
24
George G. Judge, R. Carter Hill, William E. Griffiths, Helmut Lütkepohl, and Tsoung-Chao Lee,
Introduction to the Theory and Practice of Econometrics
, John Wiley & Sons, New York, 1982, p. 621.
25
Lawrence R. Klein,
An Introduction to Econometrics,
Prentice-Hall, Englewood Cliffs, NJ, 1962, p. 101.
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