I have performed a regression examining data on crime rates. It looks at a standard ratio type variable (beginning crime rate at a point in time) and a dummy variable (if the countries crime rate is in the top mid or bottom third of beginning crime rates). We consider the effect upon the change in crime over time, crmdelta. The model code and HC standard error regression output is as follows:
df$rank.f <- factor(df$rank)
eqn1 <- lm(crmdelta ~ crmbegin+rank.f+(crmbegin*rank.f), data=df)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.57085 4.04330 0.8832 0.37839
crmbegin -0.15049 0.29486 -0.5104 0.61045
rank.f2 -3.38911 4.22533 -0.8021 0.42361
rank.f3 1.59112 4.69654 0.3388 0.73518
crmbegin:rank.f2 0.16871 0.43199 0.3906 0.69661
crmbegin:rank.f3 -3.12450 1.64205 -1.9028 0.05874 .
2 questions:
(1) I cant tell what happened to the interaction crmbegin:rank.f1. Is this represented by crmbegin? And if so, is there no lone crmbegin variable even though it was specified in the regression?
(2) How do I precisely interpret the coefficients on the interactions? Is it the effect of the ratio variable given the singular case of whichever dummy is in effect? Ie. crmbegin:rank.f2 is the marginal effect of crmbegin, given we are operating in rank.f2 data subset?
Thanks very much for any help. My first post here and looks like a great community.