Most of the interest in a regression has to do with the residuals or error
terms.
For the results to be valid we must assume that:
1.
The residuals are a sequence of independent, random variables with
mean zero and variance σ
2
.
If the residuals are correlated or if
they are not independent then we have a problem
2.
We must assume that the independent variables are either random or
given, nonrandom numbers which are distributed independently of
the error terms.
So the covariance of any given error terms must be
zero.
Are the least squares estimates a good estimate?
Yes, if the assumptions are
met.
There are 2 major problems that can occur.
The first is called
multicollinearity.
The parameters indicate the effects of independent variables on the
dependent variable.
However if the exogenous variables are correlated, then
it is still possible to estimate the effect of a single variable.
However it is
not desirable to have the independent variables correlated.
The more highly
correlated the independent variables, the more problems that we encounter
and economic variables are often highly correlated.
If variables were perfectly correlated, then our system breaks down.
If they
are highly correlated, then
1. the precision of estimates falls so that it becomes very difficult to
disentangle the individual effects of independent variables
2. coefficients which are important may appear to have no statistical
significance
3. estimates of coefficients become very sensitive to changes in the
sample used or to put it another way they can become unstable
We can test the variables to see how correlated they are, but most economics
data sets are outside the researcher’s control
The only solution for serious
multicollinearity is to try to get new data or a new method of analysis.
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View Full DocumentSecondly we have the problem of
autocorrelation.
This occurs when the
residuals are correlated with each other which violates one of the
assumptions of the model.
This results in unbiased estimates of the
coefficients but can cause severe problems with the sampling variances and
the F test.
There are a number of ways that this can be dealt with that we
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 Winter '11
 sinclair
 Regression Analysis, researcher, independent variables

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