What Is Homoskedastic?

Homoskedastic (also spelled "homoscedastic") refers to a condition in which the variance of the residual, or error term, in a regression model is constant. That is, the error term does not vary much as t🍎he value of the predictor variable changes. Another way of saying this is that the variance of the data points is roughly the same for all data points.

This suggests a level of consistency and makes it easier to model and work with the data through regression. A lack of homoskedasticity may suggest that the regression model may need to include add🌞itional predictor variables to expla꧟in the performance of the dependent variable.

How Homoskedasticity Works

Homoskedasticity is one assumption of 澳洲幸运5开奖号码历史查询:linear regression modeling, and data of this type work well with the 澳洲幸运5开奖号码历史查询:least squares method. If the variance of the errors around the﷽ regression line varies much, the regression model may be poorly defined.

The opposite of homoskedasticity is heteroskedasticity (just as the opposite of "homogenous" is "heterogeneous"). 澳洲幸运5开奖号码历史查询:Heteroskedasticity (also spelled “heteroscedasticity”) refers to a condit🐲ion in which the variance of the error term in a regression equation is not constant.

Special Considerations

A simple regression model, or equation, consists of four terms. On the left side is the dependent variable. It represents the phenomenon the model seeks to "explain." On the right side are a constant, a predictor variable, and a residual term, also known as an error term. The error term shows the amount of variability in the dependent variable that is not explained by the predictor variable.

Example of Homoskedastic

Suppose you wanted to explain st🐼udent test scores using the amount of time each student spent studying. In this case, the test scores would be the dependent variable and the time spent studying woul🧔d be the predictor variable. 

The error term would show the amount of variance in the test scores that was not explained by the amount of time studying. If that variance is uniform, or homoskedastic, then thꦐat would suggest the model may be an adequate explanation for test performance—that is, 💎that the amount of time spent studying explains the test scores.

But the variance may be heteroskedastic. A plot of the error term data ꦜmay show a large amount of study time corresponded very closely with high test scores but that low study time test scores vari﷽ed widely and even included some very high scores.

This would indicate that the variance of scores was not well-explained🅠 simply by the one predictor varꦉiable of the amount of time studying. In this case, some other factor is probably at work. The model would likely need to be enhanced to identify it or them.

Further investigation may reveal other factors that impacted scores,🐷 such as:

• Some students had seen the answers to the test ahead of time
• Students who had previously taken a similar test didn't need to study for this one
• Students had levels of test-taking skill independent of their study time

To improve on the regression model, the researcher would have to try out other explanatory variables that could provide a more accurate fit to the data. If, for example, some students had seen the answers ahead of time, the regression model would then have two explanatory variables: ti🍨me studying and whether the student had prior kn🌳owledge of the answers.

With these two variables, more of the variance of the test scores would be explained and the variance of the error term might then be homoskedastic, suggesting th♕at the model was well-defined.

The Bottom Line

In a linear regression model, homoskedasticity oꦬccurs when the variance of the error term is constant. This indicates that the model is well-defined, meaning that the dependent variable is adequately defined by the predictor variable.

If there is too much variance in the error term, the model isn't well-defined. This is known as heteroskedasticity. Too much variance indicates that there are other factors influencing the dependent variable. These factors need to be considered through further investigation or modeling.