National open university of nigeria introduction to econometrics I eco 355

3.0 
MAIN CONTENT 
 
3.1 
The Linear Regression Model 
We can ask ourselves a question that why do we regress? Econometric methods such as 
regression can help to overcome the problem of complete uncertainty and guide planning 
and decision-making. Of course, building a model is not an easy task. Models should 
meet certain criteria (for example a model should not suffer from serial correlation) in 
order to be valid and a lot of work is usually needed before we achieve a good model.
Furthermore, much decision making is required regarding which variables to include in 
the model. Too many may cause problems (unneeded variables misspecification), while 
too few may cause other problems (omitted variables misspecification or incorrect 
functional form).
 
 
3.2 
The classical linear regression model 
The classical linear regression is a way of examining the nature and form of the 
relationships among two or more variables. In this aspect we will consider the case of 
only two variables. One important issue in the regression analysis is the direction of 
causation between the two variables; in other words, we want to know which variable is 
affecting the other. Alternatively, this can be stated as which variable depends on the 
other. Therefore, we refer to the two variables as the dependent variable (usually denoted 
by Y) and the independent or explanatory variable (usually denoted by X). We want to 

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explain /predict the value of Y for different values of the explanatory variable X. Let us 
assume that X and Y are linked by a simple linear relationship: 
Where
denotes that average value of
for given
and unknown population 
parameters ‗a‘ and
(the subscript t indicates that we have time series data). Equation 
(1) is called the population regression equation. The actual value of
will not always 
equal its expected value 
There are various factors that can ‗disturb‘ its actual 
behaviour and therefore we can write actual
as: 
or 
Where
is a disturbance. There are several reasons why a disturbance exiaists: 
1.
Omission of explanatory variables: There might be other factors (other than 
) 
affecting
that have been left out of equation (III). This may be because we do 
not know. These factors, or even if we know them we might be unable to meaure 
them in order to use them in a regression analysis.
2.
Aggregation of variables: In some cases it is desirable to avoid having too many 
variables and therefore we attempt to summarize in aggregate a number of 
relationships in only one variable. Therefore, eventually we have only a good 
approximation 
of with discrepanceis that are captured by the disturbance term. 
3.
Model misspecification: We might have a smisspecified model in terms of its 
structure. For example, it might be that 
is not affected by 
, but it is affected 
by the valaue of X in the previous period (that is 
). In this case, if 
and
are closely related, the estimation of equation (III) will lead to discrepancies that 
are again captured by the error term. 
4.
Functional Misspecification: The relationship between X and Y might be non-
linear. 
5.
Measurement Errors: If the measurement of one or more variables is not correct 
then errors appear in the relationship and these contribute to the disturbance term.