Generally, yes. Let see a classical salary (Mincer) equation. Salary is a continuos variable. And you can explain salary with both, categorical variables (sex, spoken language etc.) and non categorical variables (experience, years of education, etc.) Hope it helps. Sumit Oberoi

Hi,

Categorical variables as I.Vs can be converted into dummy variables and studied.

Vero Calderón M. and Bhogaraju Anand thanks for valuable insight.

Log transformation is must for data normality, if data is positively (right) skewed.

Yes you can. If the independent variable is binary, in this case you have no problem, so if you want to know the effect of male gender, in this case you have to give code 1 for male and zero for female. But if you have three or more categories eg for residency (urban, rural, sub-urban), in this case one of them would be a reference (eg the sub-urban), and you have to make two dummy variables, and these are 'urban' and ''rural' if you considered the sub-urban as a reference.

Namir G Al-Tawil Thank you sir.

Seek your further assistance, in epidemiology studies majority of time data turn out to be rightly (positively) skewed or not normally distributed. Does Log10 transformation is the best way of transforming continuous dependent variable to be normally distributed.

I am sure you are testing normality on residuals, not actual observed variables. As you add more IVs into your regression equation, you may not have to make any transformation at all. However, if you have to transform, make sure you choose a transformation method that can be back-transformed into the original scale. Some common transformation approaches (log, box-cox) are easy to back-transform, but some are more complex (two-step transformation) than others. This way, your interpretation is more direct and meaningful. I personally do not prefer transformation approach mainly because of interpretation. There are other regression techniques that specializes in skewed distribution.

I dealt with skewed data at a government agency producing official energy statistics from establishment surveys. Skewness can make naturally occurring heteroscedasticity more noticeable. I suggest weighted least squares (WLS) regression with the regression weights built into the regression coefficients. I don't know if it will help with the problem here, but it would be a better place to start, I think. See the following:

......

Nature and magnitude of heteroscedasticity of variance of y|y*, for regressions of form y=y*+e,

for finite populations:

https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as bounded by Ken Brewer,

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

and

https://www.researchgate.net/project/OLS-Regression-Should-Not-Be-a-Default-for-WLS-Regression, and the various updates there, in reverse chronological order.

And

https://www.researchgate.net/project/Cutoff-and-quasi-cutoff-sampling-with-prediction-for-Official-Statistics, and the updates.

Cheers - Jim