[R] stat question - not R question so ignore if not interested

[Leeds, Mark (IED)]

If do a scattrplot of data ( x and y ) and there are two clouds of
points. One cloud is in the left
bottom corner of the plot and the other cloud is in the upper right.

If I fit a regression line to this data ( or equivalently , calculate a
correlation ), then obviously, it is going to seem like
x and y are related because a line has to be connected between the 2
clouds. But, there must be a regression assumption that
is violated here because if the regressions are done separately on each
cloud, then there really isn't
a relationship between x and y. I was just wondering 1) what assumption
in regression is being violated in
the first case or 2) possibly if the regression is valid and the results
just have some different interpreation ? 
Thanks.

 
Mark
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