Do you mean to say that your _dependent_ variable is binary? If so, what do you hope to determine by knowing if your data are homoscedastic or not?

If we're going to do regression then let's do it right. This is a logistic regression with a binary DV. I don't know what package you use. But download Jared Lander, R for everyone from the z-library and you find a logistic regression program that will do it for you. Try it. You'll like it. And get sensible results. An intro example can be found in Frank Harrell's book Regression Modeling Strategies also available in the z-library. Best wishes David Booth

There are quite a few technical things you need to know.

Your are in essence trying to model a latent (that is unmeasured) dependent variable, the probability of 'yes' saying, when what you have is a observed binary variable with 1 for Yes and 0 for No. You are not going to get much insight from plotting the observed data.

As others have said, you need a generalized linear model such as a logit or probit that more properly models the underlying dependent variable that is constrained to be between 0 and 1. The random (or error) term of such a model is usually not assumed to be a Normal distribution but is assumed typically to be a Bernoulli distribution in the binary case. This essentially has heteroscedasticity built in to it so that the residual variance depends on the mean predicted probability, being most variable when the predicted responses on the probability scale is around 0.5, and is least variable when the response approaches 0 and 1; there is literally less room to vary. In practice the logit- Bernoulli model takes care of this essential heteroscedasticity.

It is also possible to have additional variability which is called over-dispersion - that is overdispersion compared to the standard model - for example, you may have left out an important predictor variable, and this is being picked up in the random term. The binary model however does not have sufficient information to model this overdispersion. You can do so if you have data in the form of the proportion of Yes saying which you can fit a Logit-Binomial model with potentially an overdispersed random term. See Article Redundant Overdispersion Parameters in Multilevel Models for...

If you want some free learning materials on the logit model which goes in to the practical applications of such technical issues, see http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#discrete

I also don't understand your approch and what the aim of this analysis should be.

The binary DV cannot be homoscedastic, as its variance must depend on the mean. Hence, checking if the variance in the two groups is similar is a complcated way to check if the means are similar.

The question for a binary DV could be if the assumption makes sense that each observation is a result of a Bernoulli experiment with the same success probability (p). If this probability may be different for different observations, then you will get a larger variance than expected by the binomial model (what is called over-dispersion). In this case you should use a beta-binomial or a quasi-binomial model that can handle over-dispersion.

As Dr Jochen Wilhelm said, the distribution of the non-standard residuals (or error term) is not uniform, so you need a function, relation, or transformation to describe it. It seems that the variance of the error term is the same for the two groups.

The figure attached to the original question suggests that one variable is Customer Loyalty Behaviour (0=No, 1=Yes). Was this measured as a dichotomy originally? Or do you have some kind of scale that was coarsened into a dichotomy? And what is the other variable, that you presumably treated as the explanatory variable in your regression model? (Or variables, if there were 2 or more explanatory variables.) It would be helpful, I think, if you provided some basic descriptive stats for all variables in your model. It would also help if you spelled out your research question. HTH.

A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables. if the dots approach to the strait line or on strait line then we can say there is linear relation ship between two variable.