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

Gaussian, standard,
or
classical linear regression model (CLRM),
which is
the cornerstone of most econometric theory, makes 7 assumptions.
7
We first discuss these
assumptions in the context of the two-variable regression model; and in Chapter 7 we
extend them to multiple regression models, that is, models in which there is more than one
regressor. 
ˆ
y
i
= ˆ
β
2
x
i
7
It is classical in the sense that it was developed first by Gauss in 1821 and since then has served as a
norm or a standard against which may be compared the regression models that do not satisfy the
Gaussian assumptions.
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62
Part One
Single-Equation Regression Models
We have already discussed model (2.4.2) in Chapter 2. Since linear-in-parameter
regression models are the starting point of the CLRM, we will maintain this assumption for
most of this book.
8
Keep in mind that the regressand 
Y
and the regressor 
X
may be
nonlinear, as discussed in Chapter 2.
ASSUMPTION 1
Linear Regression Model:
The regression model is 
linear in the parameters,
though it may or may not be linear in the variables. That is the regression model as shown
in Eq. (2.4.2):
Y
i
=
β
1 
+
β
2
X
i
+
u
i
(2.4.2)
As will be discussed in Chapter 7, this model can be extended to include more explanatory
variables.
ASSUMPTION 2
Fixed 
X
Values or