Typically, heteroscedasticity influences the infetential statistics and not the parameter estimation. Therefore, you can use robust estimators like HC3 or HC4, no need to transform the Data.

What statistical package will you use to process the data? For example, with STATA you can use the vce (robust) option to obtain robust errors in the presence of heteroscedasticity

Abu -

The nature of heteroscedasticity in regressions of form y = y* + e, for finite populations, is explained here:

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity

Model and data issues can influence heteroscedasticity, either increasing or decreasing the impact, but using the format above can handle all of this, as shown in examples here:

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

To apply this to your data, first produce the OLS results, and then use the spreadsheet here:

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

For further information, please see the following:

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and updates

Cheers - Jim

Attached is the summary from "Estimating the Coefficient of Heteroscedasticity." I also included this in responses to https://www.researchgate.net/post/Is_there_heteroscedasticity_in_my_data_and_if_so_how_can_I_reduce_it

Also, please note in the project link above that one of the updates explains why using an hypothesis test for heteroscedasticity is not useful.

Abu -

You asked "If homoscedasticity criteria is not being met in regression analysis, what tools can used to make it homosedastic?"

However, the homoscedasticity 'assumption' is not really appropriate because heteroscedasticity is to be expected for finite population applications when your model and data are ideal. That is, one should expect that with larger predictions, the sigma for the estimated residuals will be larger. One can handle that using weighted least squares (WLS) regression, which uses a weight which is a measure of size, say, for practical purposes, preliminary predicted y values, raised to the -2gamma power, i.e.,

w =

(preliminary predicted y)^(-2gamma),

where gamma is the coefficient of heteroscedasticity in papers I referenced above. Now, if gamma = 0, which ideally would not happen, then the weights are equal, and we have OLS regression. Finding a good gamma value is covered in the references I already provided.

Examples are given here:

https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

A tool for finding gamma for your data is given here:

https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

If your software will let you enter regression weights, w, then it should also provide the estimated variance of the prediction error, which can be used in prediction intervals, around each prediction.

Cheers - Jim

Well, it depends on what kind of data you are working with.

Here are some simple rules:

If you have positive real values like the heights of trees, try logs, if this does not work, try Box-Cox.

If you have count data from Poisson distribution, you need sqrt(x). If doesn't work, try Box-Cox or logs.

If you have percentages (0;1), you need logit.

If you have percentages [0;1], you need Arcsin+Sqrt.

If it's something like correlation coefficients, try Fisher's z-transformation.

To create effective visualizations, let me recommend this ePoster with our guidelines:

https://www.researchgate.net/publication/343351147_A_Visual_Framework_for_Longitudinal_and_Panel_Studies_with_Examples_in_R

The above poster has some simple R codes as well.

P.S. depends on the objective of the research, you can just try using ranks to perform initial analysis as a first step to check for correlation.

Dear Abu Bashar

If the homoscedasticity hypothesis is not fulfilled, the standard errors will not be correct. You must use a robust estimation method against heteroscedasticity. What statistical software will you use? You can see:

STATA: https://www.stata.com/support/faqs/statistics/robust-standard-errors/

R: https://data.princeton.edu/wws509/r/robust

SPSS: https://www.ibm.com/support/pages/can-i-compute-robust-standard-errors-spss

Best Regards

Thank you very much@Eulogio sir. It is great help

Abu -

Predictions are impacted to some degree, though the main problem is standard errors. Instead of ignoring impact on predictions and patching the standard errors, I think it is a lot cleaner to use weighted least squares (WLS) regression. That more closely models things as they actually are.

Cheers - Jim

The WLS regression that James R Knaub suggests often does the trick if you can guess the weights (and sd rising with mean often works). Another straight forward approach is to model both the mean and the sd of the response variable. The R package lmvar does this in a fairly straight forward manner. This is useful if you aren't thinking of heteroskedaticity as just a nuisance, but you actually are interested in exploring it. More info at: https://rdrr.io/cran/lmvar/#vignettes

Abu, et.al. -

As a reminder of my earlier response, I have provided a tool for estimating regression weights.

I expect your software will let you enter w for the regression weights.

w = z^(-2 gamma)

Examples are in here: https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity

A tool for doing this with your data and model is given here: https://www.researchgate.net/publication/333659087_Tool_for_estimating_coefficient_of_heteroscedasticityxlsx

Cheers - Jim