First of all, thank you for the community; I have learnt a lot from this forum during the past week. I am completely new to statistical analysis and is hoping for some direction with my academic research project on the data analysis side of things.

I am working on a research project to identify the impact of dominant personalities, and sexual esteem on sadistic behavior. Both of my independent and dependent variables have been measured using standard questionnaires used in the field of research

* IV Dominance (4 point Likert scale): Hamby, 1996

* IV Sexual Esteem (5 point Likert scale): Snell and Papini, 1989

* DV Sadistic Behavior (1/0 dichotomous scale): Freund, Stein, & Chan, 1982

A given respondent's responses were summed to obtain a single score for each measure (I realize that this is debatable, but similar studies have followed the same scoring approach and I have decided to do the same). The Cronbach's alpha for the scales are consistent with the original studies and is well over 0.70.

Both Pearson's and Spearrman correlation coefficients are really low. The next step I was planning on taking was to run a linear regression analysis on my two IV separately against the DV. However, the problem right now is my dependent variable violates regression assumptions (linearity, residual variance) with the independent variable (see attached scatter plot). As far as I can see, a linear regression analysis is not possible. Playing around with SPSS and curve fitting I found out that a logarithmic curve fits the data slightly better, but I don't see how I can interpret a non-linear regression analysis for my data set in any meaningful way.

My questions are:

1. Have I missed any steps that could improve my analysis?

2. Is there any other approach that I can consider? I looked into non-parametric approaches but most of them seem to find relationships across groups, which is not what I need.

3. It could just be that my hypothesis is not supported by the data; In that case, is it sufficient to just use Person's (or Spearman) correlation data for hypothesis testing? It feels very inadequate.

4. If I find relationships in my data outside of my hypothesis (eg: sadistic behavior is prevalent in a certain gender or age group) can I still document this in my research paper?