The crucial assumption of a classical linear regression model is that the volatility that has occurred in the model should be uniform in nature. If this assumption is not satisfied by the model, then one would have to consider that the model has been exposed to heteroscedasticity.
There are examples that can be discussed to gain a better understanding of heteroscedasticity. In the case of an income expenditure model, if the income is decreased, then the expenditure will also simultaneously decrease, and vice versa. If, however, heteroscedasticity is present in the model, then as the income is increased, then the graph for the expenditure variable would remain constant.
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Heteroscedasticity generally occurs due to the presence of an outlier. An outlier in relation to heteroscedasticity is nothing but an observation that is numerically apart from the rest of the observations given in the data.
Heteroscedasticity can occur if a major variable is eliminated from the model. In the case of the income expenditure model, for example, if the variable called ‘income’ is eliminated, then there would be no inference from that model, and one would have to consider that the model has undergone heteroscedasticity.
Heteroscedasticity can also occur due to the presence of symmetrical or assymeterical curves of the regressor included in the model.
Heteroscedasticity can also occur due to false data transformation and incorrect functional form (like comparisons between a linear model and a log linear model, etc.).
Heteroscedasticity is a common or popular type of disturbance, especially in cases involving cross sectional data or time series data. If investigators who conduct ordinary least squares (OLS) do not consider the disturbance caused by heteroscedasticity, then they would not be able to examine the confidence intervals and the tests of hypotheses. This is because in the presence of heteroscedasticity, the variance calculated would be significantly less than the variance of the best linear unbiased estimator. As a result, the outcomes of the significant tests will not be accurate due to heteroscedasticity.
For a researcher to detect the presence of heteroscedasticity in the data, certain informal tests have been proposed by several econometricians.
There is a high probability of heteroscedasticity in a cross sectional data if small, medium and large organizations are sampled together.
An informal method, called the graphical method, helps the researcher to detect the presence of heteroscedasticity. If the investigator assumes that there is no heteroscedasticity and then performs regression analysis, the estimated residuals (with the help of the graphical method) would then exhibit certain patterns that would indicate the presence of heteroscedasticity.
A formal test, called Spearman’s rank correlation test, is used by the researcher to detect the presence of heteroscedasticity.
Suppose the researcher assumes a simple linear model, for example- Yi = β0 + β1Xi + ui - to detect the presence of heteroscedasticity. The researcher then fits the model to the data by calculating the absolute values of the residual and further sorting them in ascending or descending manner to detect heteroscedasticity. Then, the researcher computes the value of Spearman’s rank correlation for heteroscedasticity.
The researcher then assumes the population rank correlation coefficient as zero and the size of the sample is assumed to be greater than 8 for heteroscedasticity. 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.
