# Interaction effects and insignificant main effects - Back to basics

Imagine the following regression model:

$\text{Abnormal Returns} = b0 + b1*SENT + b2*SIZE + b3*SENT*SIZE + e$

SENT is a standardized variable. SIZE is equal to 1 for "uncertain" firms, and 0 for certain firms.

I am examining whether sentiment affects abnormal returns more or less when firms are classified as uncertain or certain. Now, I have run the regression model and I understand how to interpret the results when ALL coefficients are significant and it is as follows:

(1) when there is no sentiment (SENT=0), the abnormal returns increases with b0 for firms classified as certain (SIZE=0, SENT*SIZE=0).

(2) when there is No sentiment (SENT=0), the abnormal returns increases with b0+b2 for firms classified as uncertain (SIZE=1, SENT*SIZE=0).

(3) when sentiment is high/low (SENT= 1 SD above mean or 1 SD below mean), the abnormal returns increases/decreases with b1 for firms classified as certain (SIZE=0, SENT*SIZE=0).

(4) when sentiment is high/low, the abnormal returns increases/decreases with b1+b2+b3 for firms classified as uncertain (SIZE=1, SENT*SIZE=1).

I have some doubts on how and if to interpret the results if only some coefficients are significant. Thus my questions are:

1. Should I interpret the results if only b1(SENT) is significant? How do I interpret this?

2. Should I interpret the results if only b2(SIZE) is significant? How do I interpret this?

3. If only the interaction effect is significant, how do I interpret this?

So lets suppose you find only $\beta_3$ is significant in your results. I would still report all the estimated effects, but also note that we had only found enough evidence to conclude that SENT has a positive effect with firms of SIZE = 1.
In terms of interpreting insignificant results, let's use the example that $\hat \beta_1 = 1$, but is insignificant: "We observed that in our sample, the average abnormal returns from firms of SENT = 1 with SIZE = 0 was 1 higher than the average of abnormal returns from firms with SENT = 0 and SIZE = 0. However, we did not observe enough evidence to conclude that this was a real systematic difference between these two groups, rather than the possibility of random chance".
• You should definitely include $\beta_1$ (the estimated main effect of SENT), even though it is not statistically significant, when reporting the estimated value for when SIZE = 1 and SENT = x. – Cliff AB Jun 12 '15 at 18:20