# How to interpret linear regression in scatter plot

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?

• In your opinion, is the bimodal distribution of the dependent variable ($y$) affecting in some way my regression? I would say this is not important from the regression point of view, but I would like to know if the bimodal distribution can introduce some problems. – gc5 Dec 1 '16 at 11:11