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

exact linear relationship
between 
X
2
and 
X
3
(7.1.9)
In Section 7.7, we will spend more time discussing the final assumption.
9. There is no 
specification bias
.
The model is correctly specified.
(7.1.10)
The rationale for assumptions (7.1.2) through (7.1.10) is the same as that discussed in
Section 3.2. Assumption (7.1.9), that there is no exact linear relationship between 
X
2
and
X
3
, is technically known as the assumption of 
no collinearity
or 
no multicollinearity
if
more than one exact linear relationship is involved.
Informally, no collinearity means none of the regressors can be written as 
exact
linear
combinations of the remaining regressors in the model.
Formally, no collinearity means that there exists no set of numbers, 
λ
2
and
λ
3
, not both
zero such that
λ
2
X
2
i
+
λ
3
X
3
i
=
0
(7.1.11)
ASSUMPTIONS
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Part One
Single-Equation Regression Models
If such an exact linear relationship exists, then 
X
2
and
X
3
are said to be 
collinear
or
linearly dependent. On the other hand, if Eq. (7.1.11) holds true only when 
λ
2
=
λ
3
=
0, then 
X
2
and 
X
3
are said to be 
linearly independent.
Thus, if
X
2
i
= −
4
X
3
i
or
X
2
i
+
4
X
3
i
=
0