What Is Homoskedastic?

In a regression model, homoskedasticity (also known as “Homoskedastic”) occurs when the variance of the residual, or error term, is constant. The error term varies little as the predictor variable changes. Another explanation is that all data points have a similar variance.

This implies consistency and makes regression easier, but the lack of homoskedasticity may signal that the regression model needs more predictor variables to explain the dependent variable’s performance.

How Homoskedasticity Works

The least squares approach performs well with homoskedastic data, an assumption of linear regression modeling. If the variation of errors around the regression line is significant, the regression model may be poorly specified.

The opposite of “homogenous” is “heterogeneous.” Heteroskedasticity (also known as “heteroscedasticity”) occurs when the variance of the error factor in a regression equation is not constant.

Special Considerations

A four-term regression equation is straightforward. Dependent variable on the left. The model aims to “explain.” Right side: constant, predictor variable, residual, or error term. The error term represents the dependent variable’s variability, which the predictor does not account for.

Homoskedastic example

For instance, you may explain student test scores using study time. Test results are the dependent variable, and study time is the predictor.

The error term would reveal a test score variance not explained by studying time. The model may explain test performance by focusing on study time if the variance is uniform or homoskedastic.

But the variance may be heteroskedastic. A plot of error-term data may demonstrate that high exam scores were strongly related to study time. In contrast, poor test scores fluctuated considerably and even contained some extremely high scores.

Thus, one predictor variable—study time—would not explain score variation. We may need to improve the model to uncover another component in this scenario.

Homoskedasticity can help establish which elements need to be changed for accuracy when variance is the measured difference between an event’s expected and actual result.

Further inquiry may reveal that some students saw the exam answers beforehand or have taken a comparable test. Thus, they didn’t need to study. Pupils might also have varying test-passing capacities regardless of subject, study time, or past test results.

To enhance the regression model, the researcher must explore alternative explanatory variables that suit the data better. For example, if some students had pre-viewed answers, the regression model would include two variables: study time and previous knowledge.

These two variables would explain more test score variation and make the error term homoskedastic, indicating a well-defined model.

The Meaning of Heteroskedasticity

Statistic heteroskedasticity is error variance. A sample with at least one independent variable has this dispersion dependency. The standard deviation of a predictable variable is non-constant.

Homoskedastic Regression: How to Tell?

See if a regression is homoskedastic by comparing its highest and most minor variances. If the ratio is 1.5 or less, the regression is homoskedastic.

Why does homoskedasticity matter?

An essential aspect of homoskedasticity is identifying population differences. Uneven variance in a population or sample will give skewed or biased results, rendering the study useless.

Conclusion

• Homoskedasticity arises when a regression model’s error term variance is constant.
• If the error term variance is homoskedastic, the model is well-defined. The model may be poorly defined if the variation is high.
• Additional predictor factors can explain dependent variable performance.
• In contrast, heteroskedasticity arises when error term variance varies.