Hello Nasim,

While a huge number of predictors argues for a big sample size, it's not the number of predictors that governs whether model residuals are homoscedastic or not. The check is done in the same way with one predictor or 1,000 predictors.

1. Fit the model

2. Compute/save the residuals for all cases.

3. Plot residuals (usually standardized, by dividing by standard error of estimate) against predicted values.

4. Inspect plot for absence of pattern.

OR...

Apply a formal test, like Breusch-Pagan, or some alternative.

Good luck with your work.

Hello David,

Thank you very much for the valuable information.

Nasim -

Heteroscedasticity in regression is to be expected. See https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, regarding regressions of form y = y* + e. However, model and data issues can cause heteroscedasticity to be effectively either enhanced or reduced.

If you have OLS regression results, https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity will show you how to find how much heteroscedasticity (if any) the data are estimated to be exhibiting. Several examples are shown. You can do this with your own data using the following tool: https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

For further information, please see https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression and the various updates to that project.

Cheers - Jim

PS - You may have indicated doing many one-regressor models. I suspect you will often find substantial heteroscedasticity, in the range that Ken Brewer justified (see https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity). However, some of your models may not work well, and if you try any multiple regressions, and overfit, I suspect this might cause low or basically no heteroscedasticity. Perhaps you meant univariate as opposed to multivariate regression, so you are talking about many independent variables. Regardless, you can use the tool given above.

PSS - Regarding sample size, a larger sample size will allow you to better estimate the coefficient of heteroscedasticity (the level/degree/amount of heteroscedasticity). In that sense it is like a standard deviation of a population, rather than like the standard error of an estimated mean. A larger sample does not change it systematically. It just estimates it better.