[SciPy-user] Limits of linrgress - underflow encountered in stdtr

[David Warde-Farley]

On 9-Jun-09, at 2:21 PM, wierob wrote:

> So, for now I assume that linregress works as it should. Also, I don't
> understand why ignoring these errors is ok.

Because the underflow doesn't change the answer enough to make any  
conceivable difference.

Underflow just means that some quantity that was computed was too tiny  
to be represented, in which case it is effectively 0.

It's notable that R reports "p-value < 2.2e-16", which is machine  
epsilon in 64-bit floating point, i.e. a bound on the relative error  
due to rounding. I'd read that as R thinking that the P-value is  
probably garbage and rounding error dominates (and will vary with the  
exact formula used), but "less than 2.2e-16" is still small enough to  
be considered "statistically significant" by any wild stretch of the  
imagination.

David