# Heteroscedasticity

Quantitative Results
Statistical Analysis

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. Outlier in Heteroscedasticity means that the observations that are either small or large with respect to the other observations are present in the sample.

Heteroscedasticity is also caused due to omission of variables from the model. Considering the same income saving model, if the variable income is deleted from the model, then the researcher would not be able to interpret anything from the model.

Heteroscedasticity is more common in cross sectional types of data than in time series types of data. If the process of ordinary least squares (OLS) is performed by taking into account heteroscedasticity explicitly, then it would be difficult for the researcher to establish the process of the confidence intervals and the tests of hypotheses. Due to the presence of heteroscedasticity, the variance that is obtained by the researcher should be of lesser value than the value of 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 heteroscedasticity.

A formal test called Spearman’s rank correlation test is used by the researcher to detect the presence of heteroscedasticity. This test can be used in the following way. Suppose the researcher assumes a simple linear model, Yi = ß0 + ß1Xi + ui, to detect heteroscedasticity. 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 heteroscedasticity. After this, the researcher computes the Spearman’s rank correlation for heteroscedasticity. Moving on to the heteroscedasticity detection process, the population rank correlation coefficient is assumed as 0 and the size of the sample is assumed to be greater than 8. A significance test is carried out to detect heteroscedasticity. 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.