[R] Standard errors in regression models with interactions terms

[rm]

In a rather simple regression, I’d like to ask the question, for high trees,
whether it makes a difference (for volume) whether a three is thick.

If my interpretation is correct, for low trees, i.e. for which trees$isHigh
== FALSE, the answer is yes. 

The problem is how to "merge" the standard errors. Code follows.

data(trees)
trees$isHigh <- trees$Height > 76
trees$isThick <- trees$Girth > 13
m <- lm(trees$Volume ~ trees$isHigh + trees$isThick +
trees$isHigh:trees$isThick)
summary(m)

I might be mistaken, but a workaround is to rewrite the model as follows,
which shows that the answer is yes. However, I would very much like to know
how to answer the question with the original model.

data(trees)
trees$isLow <- trees$Height <= 76
trees$isThick <- trees$Girth > 13
m <- lm(trees$Volume ~ trees$isLow + trees$isThick +
trees$isLow:trees$isThick)
summary(m)








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