Heteroscedasticity
An important assumption assumed by the classical linear regression model is that the error term should be homogeneous in nature. Whenever that assumption is violated, then one can assume that heteroscedasticity has occurred in the data.
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An example can help better explain Heteroscedasticity.
Consider an income saving model in which the income of a person is regarded as the independent variable, and the savings made by that individual is regarded as the dependent variable for heteroscedasticity. So, as the value of the income of that individual increases, simultaneously the savings also increase. But in the presence of heteroscedasticity, the graph would depict something unusual— for example there would be an increase in the income of the individual but the savings of the individual would remain constant.
This example also signifies the major difference between heteroscedasticity and homoscedasticity. Heteroscedasticity is mainly due to the presence of outlier in the data. An outlier refers to observations that are significantly smaller or larger than others in the sample.
Omitting variables from the model causes heteroscedasticity. For example, if a researcher deletes the income variable from the income-saving model, they cannot interpret the model’s results.
Heteroscedasticity is more common in cross sectional types of data than in time series types of data. When researchers account for it in OLS, they struggle to establish confidence intervals and hypothesis tests. Due to it, the variance obtained is lower than the variance of the best linear unbiased estimator (BLUE). Therefore, the results obtained by the researcher through significant tests would be inaccurate because of the presence of heteroscedasticity.
Let us discuss some informal tests to detect the presence of it.
Researchers use Spearman’s rank correlation test to detect it. They apply the test as follows. Suppose the researcher assumes a simple linear model, Yi = ß0 + ß1Xi + ui, to detect it. The researcher then fits the model to the data by obtaining the absolute value of the residual and then ranking them in ascending or descending manner to detect it.
After this, the researcher computes the Spearman’s rank correlation for heteroscedasticity. In the heteroscedasticity detection process, researchers assume the population rank correlation coefficient is 0 and the sample size is greater than 8. They then carry out a significance test to detect it. If the computed value of t is more than the tabulated value, then the researcher assumes that heteroscedasticity is present in the data. Otherwise, heteroscedasticity is not present in the data.