1030 Words5 Pages

The Heteroskedasticity Problem in Regression Analysis
Recall that one of the assumptions of the OLS method is that the variance of the error term is the same for all individuals in the population under study. Heteroskedasticity occurs when the variance of the error term is NOT the same for all individuals in the population. Heteroskedasticity occurs more often in cross-section datasets than in time-series datasets.
Consequences of Heteroskedasticity:
1. the estimates of the b’s are still unbiased if heteroskedasticity is present (and that’s good),
2. but, the s.e.’s of the b’s will be biased, and we don’t know whether they will be biased upward or downward, so we could make incorrect conclusions about whether the X’s affect Y
3. the estimate of S.E.R. is biased, so we could make incorrect conclusions about model fit
Detecting Heteroskedasticity:
1. Plot the regression residuals/errors, the “ehats,” or the squared residuals, the "ehats-squared", against the X variables (you should plot the residuals against each X variable separately to check which of the X variables might be a source of Heteroskedasticity).
a. If Heteroskedasticity is not present, the variation in the ehats around (above and below) zero will be the same for all values of X. Figures 1a and 1b below are examples of residual plots when Heteroskedasticity is NOT present.
b. If Heteroskedasticity is present, the variation in the ehats will not be the same for all values of X. Figures 2a and 2b are examples of residual plots when Heteroskedasticity IS present.
2. A more sophisticated statistical test such as the Park test, Breusch-Pagan test, Glejser test, White test, etc. (we do not cover these tests in this course).
Correcting a Regression Analysis for Heteroskedasticity:
If Heteroskedasticity is present, we can

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