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Homoscedasticity equal error variance

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One of the assumption of OLS regression is that error terms have a constant variance across all value so f independent variable. If not heteroscadisticity.

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standard errors underestimated so t ratos are larger More common in cross sectional data than time series data

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Heteroskedasticity implies that the variances (i.e. - the dispersion around the expected mean of zero) of the residuals are not constant, but that they are different for different observations. This causes a problem: if the variances are unequal, then the relative reliability of each observation (used in the regression analysis) is unequal. The larger the variance, the lower should be the importance (or weight) attached to that observation.

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Homoscedastic disturbances.

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Heteroscedastic disturbances.

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Note that the problem of heteroscedasticity is likely to be more common in cross-sectional than in time series data. In cross-sectional data, one

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Detection of Heteroscedasticity Graphical methods: Looking for patterns in the plot of the predicted dependent variable and the residual Formal tests: One of the best is White’s general test for heteroscedasticity. If the graphical inspection hints at heteroskedasticity, you must conduct a formal test like the White’s test.

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No problem

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Consequences of Using OLS in the Presence of Heteroscedasticity OLS estimation still gives unbiased coefficient estimates, but they are no longer BLUE. This implies that if we still use OLS in the presence of heteroscedasticity, our standard errors could be inappropriate and hence any inferences we make could be misleading. Whether the standard errors calculated using the usual formulae are too big or too small will depend upon the form of the heteroscedasticity. In the presence of heteroscedasticity, the variances of OLS estimators are not provided by the usual OLS formulas. But if we persist in using the usual OLS formulas, the t and F tests based on them can be highly mislead- ing, resulting in erroneous conclusions

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solve Use logarithm of dependent variable Use other method than OLS

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SPSS

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Statistics 350 Lecture 17. Today Last Day: Introduction to Multiple Linear Regression Model Today: More Chapter 6.

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