# Interaction are not significant for model and coefficients, but main effect is significant

I am doing a social science research on behaviour. A purchase intention. I have intention to purchase as dependent variable, attitude as predictor and extraversion as moderator.

DV = intention to purchase
step 1
attitude (center)
extraversion (center)
step 2
Attitude X extraversion (center)


The model summary show significant only in model 1 with very little R-Square change (0.003), model 2 non-significant.

The ANOVA show significant for both (0.000).

The Coefficients show significant only for attitude. The extraversion only show non-significant. The interaction Attitude X extraversion show non-significant.

But when I try to plot a High-Low graph. They are not parallel and show some cross together.

What should I interpret this? Can I interpret the graph with Non-Significant interaction-term?

Thank you very much.

You can interpret it however you want. If you leave in the interaction, you interpret the interaction. If you take it out, you don't interpret the interaction.

I'm assuming by a "high-low graph" you mean you fit a separate model for "high extraversion" and "low extraversion" people and plot both over the data. If that's what you mean, and you're wondering why you find a graphical interaction, it's because you have essentially assumed that an interaction coefficient exists. Then OLS just tried to estimate one for you.

"Nonsignificant" doesn't always mean "close to zero." It means "indistinguishable from random noise about zero." Therefore you can have a very large coefficient that is also nonsignificant, if your data is very noisy (or you have very few data points). "Nonsignificant" also does not mean "definitely due to noise." It just means you can't rule out the possibility that it's due to noise. So maybe the interaction does exist in principle but for whatever reason, maybe a small sample, it's not coming through.

In your case, because you're trying to make a prediction, I would just go with whichever model fits your data best. If the best model is a univariate linear regression, so be it. You interpret the results you have, not the results you think you should have.

Also remember that a linear regression is rarely "wrong" in the sense that the error term will always account for your misspecification. This is a problem if you want to find the "true" parameter for some theoretical model, but it doesn't seem like that's what you want. You're estimating a conditional mean around which your data varies.

Apologies if I misinterpreted what you're asking.

• Thank you for your suggestion. I am the one who should apologies for my poor level of English. You understand my point correctly. I have only 149 sample size which divide into 2 group for comparison between group 87 and 62. I think this is why it is NS. So I will report it as NS but I will draw some conclusion from the graph that compare of 2 groups. Is this will work?\ – Charnsak Dec 16 '13 at 8:59
• That's generally a safe thing to do, as long as you clearly state why you conclude what you conclude. However your sample is large enough that you shouldn't have a problem due to small N. I'd like to see the graph you're talking about, I'm still not sure what you're describing. Are you just coloring data points by "high" and "low" or are you plotting the fitted values from separate regressions? – shadowtalker Dec 16 '13 at 15:34
• I just plot the interaction graph based on the Coefficient. Use the -1SD, 0SD, +1SD for determining high, moderate, Low – Charnsak Dec 16 '13 at 19:30
• Ok. In that case, make sure you understand my point about how assuming that the coefficient exists will actually force it to exist. A better method would be to plot the actual data points you have, not the predicted values, and color them differently based on the extraversion score. This will give you a visual sense of how the groups are divided without actually imposing your modeling assumptions on the data. Then you can decide whether an interaction is justified. Multi-color plotting is very easy in Excel or R. – shadowtalker Dec 16 '13 at 20:00