I have understood why it's a bad idea having highly correlated predictors, what is puzzling me is a meaningful interpretation of moderately correlated predictors ($r< 0.3$). Let's suppose we have fitted the following linear model to some data after highly correlated predictors have been removed: $$ y = c_1x_1 + c_2x_2 + c_3x_3 + c_4x_4 + c_5x_5 $$ (For simplicity the intercept is assumed to be $0$.)
My understanding is that a way of reporting the above model would be something like:
unit change in predictor $x_3$ will results in a $c_3$ change in $y$.
However it seems to me that if predictors are moderately correlated and there are enough of them a unit change in $x_3$ in reality will correspond to a change in the other predictors and so the effect on $y$ could end up being completely different.This simply because a pure unit change in $x_3$ cannot happen without the other predictors changing due to correlation. Because of this fact I cannot see how this interpretation can be meaningful when applied to reality.
Could anybody clarify how to meaningfully report such models? I have misunderstood something perhaps?