Problems with regressions

# Problems with regressions - Most of the interest in a...

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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, non-random 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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Secondly 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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Problems with regressions - Most of the interest in a...

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