I am trying to understand the relationship between $2$ variables in $4$ different subgroups.
I would like to decide if the variables are correlated in a different way depending on the subgroup. For this reason I plotted $4$ scatter plots with a linear regression. Each scatter plot represent how the $2$ variables behave in a different subgroup (from left to right).
I would like to understand, from the scatter plot, if it is possible to assess that:
- The outliers seem to not be affecting the linear regression
- The homoscedasticity of the distribution seems good
- I may use a Pearson's r also if one of the two variables has a bimodal distribution (y-value)
- The 4th group has a positive correlation while the others have a negative correlation
Do these assessments hold? Are there more insights that I can get from these plots, or can I use different plots in this case? Would you use the Pearson's r correlation in this case or refer to another kind of correlation? Any other comments?