Interpretation of an Interaction Variable in a Quadratic Regression


New Member
Hello everyone,

this is my first post in this forum and I really hope you can help me with the interpretation of my data. I am currently writing my Master Thesis on the effects of confidence (CONF) and narcissism (NAR) on performance and risk-taking. I predicted a u-shaped relationship between CONF and performance and a moderating effect of NAR on this relationship so that performance gets worse if CEOs are narcissistic.

After running the regression, I got the following result:

Model 1 (without interaction variable):

CONF: B=0.06, p=0.838
CONF²: B=-0.278, p=0.27
NAR: B=-0.252, p=0.27

Model 2 (with interaction variable):

CONF: B=0.044, p=0.879
CONF²: B=-0.434, p=0.109
NAR: B=-0.455, p=0.089
NAR*CONF²: B=0.712, p=0.122

As you can see, all my relationships are insignificant on the 0.05 level. However, I got a slightly significant relationship between NAR and performance (p=0.089) when my interaction variable is included which is in turn not significant (p=0.122). My questions are therefore:

- Did I built up the model correctly (i.e. adding a squared IV to predict a curvilinear relationship and then subsequently adding an interaction with the squared IV?)
- In how far can the slight significance of NAR be explained while the interaction term is not significant?
- Can you give me general indications on how to interpret those figures (i.e. what does the 0.089 p-value for NAR indicate exactly)?

I hope you can help me and forgive me for not being an expert in statistics. I read a lot of things in books and relevant websites but I just did not find any examples of quadratic regressions with interaction variables!

Thanks a lot,