I have a dataset (N = 158) and the following variables that I am going to put into a regression model:
- Y (a continuous dependent variable)
- X (a continuous predictor)
- Z (a continuous predictor)
- GENDER (a binary predictor)
Initially, it was pretty straightforward that I just simply needed to use linear regression analysis to analyze this data. Before modeling, however, I found that the variable of GENDER (male [n=110], female [n=48]) has an unequal variance in my dependent variable of Y as indicated by a significant Levene's Test for Equality of Variances, and this result indicates a violation of homoscedasticity.
I'm not sure if I understood this case correctly, but based on my knowledge, in such a case I will need to add GENDER as a covariate into the model to control for its impact (please correct me if I was wrong). However, due to its unequal variance, I probably need to do some transformation for GENDER before modeling as GENDER does violate the assumption of homoscedasticity. If my understanding of above statement was correct, here are my questions:
First, can I do Logarithmic Transformations to a binary variable (GENDER) in this case?
Second, after the issue of violation of homoscedasticity was addressed, I wonder if I could use dummy-variable regression to run analysis in my case (assuming no interaction) or I have to use ANCOVA?
THANKS IN ADVANCE FOR YOUR TIME, GREATLY APPRECIATED!!