lm and R-squared (newbie)

Hello,

I've two data.frames (data1 and data4), dec="." and sep=";".
http://r.789695.n4.nabble.com/file/n4199964/data1.txt data1.txt
http://r.789695.n4.nabble.com/file/n4199964/data4.txt data4.txt

When I do
plot(data1$nx,data1$ny, col="red")
points(data4$nx,data4$ny, col="blue")
, ?results seem very similar (at least to me) but the R-squared of
summary(lm(data1$ny ~ data1$nx))
and
summary(lm(data4$ny ~ data4$nx))
are very different (0.48 against 0.89).

Could someone explain me the reason?

To be complete, I am looking for an simple indicator telling me if it is
worthwhile to keep the values provided by lm. I thought that R-squared could
do the job. For me, if R-squared is far from 1, the data are not good enough
to perform a linear fit.
It seems that I'm wrong.

# R^2 based on Pearson correlations
cor(fitted(lm(ny ~ nx, data4)), data4$ny)^2

cor(fitted(lm(ny ~ nx, data1)), data1$ny)^2

# R^2 based on Spearman (rank) correlations
cor(fitted(lm(ny ~ nx, data4)), data4$ny, method = "spearman")^2

cor(fitted(lm(ny ~ nx, data1)), data1$ny, method = "spearman")^2