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r
2
for Regression-through-Origin Model
As just noted, and as further discussed in Appendix 6A, Section 6A.1, the conventional
r
2
given in Chapter 3 is not appropriate for regressions that do not contain the intercept. But
one can compute what is known as the
raw
r
2
for such models, which is defined as
raw
r
2
=
X
i
Y
i
2
X
2
i
Y
2
i
(6.1.9)
Note:
These are raw (i.e., not mean-corrected) sums of squares and cross products.
Although this raw 
r
2
satisfies the relation 0
<
r
2
<
1, it is not directly comparable to the
conventional 
r
2
value. For this reason some authors do not report the 
r
2
value for zero
intercept regression models.
Because of these special features of this model, one needs to exercise great caution in
using the zero intercept regression model. 
Unless there is very strong a priori expectation,
one would be well advised to stick to the conventional, intercept-present model. This has a
dual advantage. First, if the intercept term is included in the model but it turns out to be sta-
tistically insignificant (i.e., statistically equal to zero), for all practical purposes we have a
regression through the origin.
4
Second, and more important, if in fact there is an intercept
in the model but we insist on fitting a regression through the origin, we would be commit-
ting a 
specification error.
We will discuss this more in Chapter 7.
3
For additional discussion, see Dennis J. Aigner, 
Basic Econometrics
, Prentice Hall, Englewood Cliffs, NJ,
1971, pp. 85–88.
4
Henri Theil points out that if the intercept is in fact absent, the slope coefficient may be estimated
with far greater precision than with the intercept term left in. See his 
Introduction to Econometrics
,
Prentice Hall, Englewood Cliffs, NJ, 1978, p. 76. See also the numerical example given next.
5
These data, originally obtained from
DataStream
databank, are reproduced from Christiaan Heij et al.,
Econometrics Methods with Applications in Business and Economics,
Oxford University Press, Oxford,
U.K., 2004.
EXAMPLE 6.1
Table 6.1 gives data on excess returns 
Y
t
(%) on an index of 104 stocks in the sector of
cyclical consumer goods and excess returns 
X
t
(%) on the overall stock market index for
the U.K. for the monthly data for the period 1980–1999, for a total of 240 observations.
5
Excess return refers to return in excess of return on a riskless asset (see the CAPM model).
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