[R-sig-eco] draw 95% confidence limits for non significant regression lines

[Paolo Piras]

Dear list,
I write for a surely trivial doubt about plotting 95% CI of regression lines. 
I saw that someone draw them even for non significant regression lines. I think that this is not correct 
as , in the majority of cases, Ho is that beta is not significantly different from 0 and consequently the observed beta is just due to chance.  
On the other hand one could argue that 95% CI limits are still informative about the distribution of the data. 

Thanks in advance for an opinion.
regards
paolo