# Interpret significant interaction with nonsignificant main term in regression involving continuous time variable and a bounded (0-100%) variable?

Scenario: I have data comparing the number of tree stems in 30 forest plots between two sampling years (1992 and 2012). Each plot received hurricane damage between these 2 sampling years -- this damage was coded as being 0-100% of trees felled/damaged.

I ran a linear regression using lm() in R including a centered year term, hurricane damage, and an interaction term between them.

I get the following output:

Call:
lm(formula = Count.Ha ~ I(Year - 1992) * HurrDam, data = dataset, ])

Residuals:
Min      1Q  Median      3Q     Max
-368.84  -69.79  -23.01   81.30  413.28

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)            147.3300    50.7297   2.904  0.00529 **
I(Year - 1992)         -17.2595     3.4007  -5.075 4.73e-06 ***
HurrDam                 -1.4680     1.6764  -0.876  0.38503
I(Year - 1992):HurrDam   0.7634     0.1128   6.766 9.11e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 138.1 on 55 degrees of freedom
Multiple R-squared:  0.5886,    Adjusted R-squared:  0.5662
F-statistic: 26.23 on 3 and 55 DF,  p-value: 1.15e-10


As you can see, Year is significant as is the interaction term, but HurrDam is not. How do I interpret this??

• I've seen a number of posts discussing intepretation when discreet variables or even continuous non-bounded variables are involved, but I'm not sure how my inclusion of a time variable and a bounded percentage as a variable impact the way one would interpret these results.

• Note: my ultimate hypothesis I'm trying to investigate is that the number of stems did not increase with time except in plots with greatest hurricane damage.

• stats.stackexchange.com/questions/22680/… Apr 10 at 17:26
• stats.stackexchange.com/questions/62921/… Apr 10 at 17:27
• And see this page. The "main effect" of a predictor involved in an interaction depends on how the interacting predictor is coded. Try changing the 1992 reference year over a wide range and see how the "main effect" for HurrDam changes. Also, with a count outcome variable you perhaps should be using a count-based generalized linear model (Poisson, negative binomial) instead, and in either case a mixed model or robust coefficient (co)variance estimates if you are evaluating the same plots over time.
– EdM
Apr 10 at 18:29
• stats.stackexchange.com/questions/593652/… Apr 10 at 18:34