Re: regr_slope returning NULL

On Sun, 24 Mar 2019 at 08:01, Steve Baldwin <steve(dot)baldwin(at)gmail(dot)com> wrote:
>
> Thanks Tom,
>
> I've tried this on 11.2 (OS X 10.14.3, installed locally) and 10.6 (AWS RDS) instances with identical results. The values you show are identical to those returned by Oracle so that's great but why am I seeing different results?
>

This is caused by the large magnitude of the ts values, which causes a
cancellation error in the Sxx calculation, which is what commit
e954a727f0 fixed in HEAD, and will be available in PG12 [1].

You can see that by including regr_sxx in the results. With PG11, this
gives the following:

select id, regr_slope(elapsed, ts) as trend, regr_sxx(elapsed, ts) as sxx
from sb1 group by id;

id | trend | sxx
------+----------------------+-------------
c742 | | 0
317e | | 0
5fe6 | 5.78750952760444e-06 | 19905896448
3441 | | 0
(4 rows)

Those zeros for Sxx are the result of calculating the sum of the
squares of ts values and then subtracting off the square of the mean,
which results in a complete loss of accuracy because the intermediate
values are so large they don't differ according to double precision
arithmetic.

A workaround in PG11 is to just offset the ts values by something
close to their mean (offsetting the ts values by a constant amount
shouldn't affect the mathematical result, but does eliminate the
cancellation errors):

select id, regr_slope(elapsed, ts-1552892914) as trend,
regr_sxx(elapsed, ts-1552892914) as sxx
from sb1 group by id;

id | trend | sxx
------+----------------------+--------------------
c742 | 19.6077357654714 | 0.0468182563781738
317e | -1.08385104429772 | 59.2381523980035
5fe6 | 5.78750948360697e-06 | 19905896596.7403
3441 | -3.82839508895523 | 20.1098628044128
(4 rows)

For PG12 the algorithm for calculating these quantities has been
changed by e954a727f0, so the result should be more accurate
regardless of the offset:

select id, regr_slope(elapsed, ts) as trend, regr_sxx(elapsed, ts) as sxx
from sb1 group by id;

id | trend | sxx
------+----------------------+--------------------
c742 | 19.6078587812905 | 0.0468179252929986
317e | -1.0838511987809 | 59.2381423694815
5fe6 | 5.78750948358674e-06 | 19905896596.7605
3441 | -3.82839546309736 | 20.1098619909822
(4 rows)

select id, regr_slope(elapsed, ts-1552892914) as trend,
regr_sxx(elapsed, ts-1552892914) as sxx
from sb1 group by id;

id | trend | sxx
------+----------------------+--------------------
c742 | 19.6078431374563 | 0.0468179999990382
317e | -1.08385109620679 | 59.2381495556381
5fe6 | 5.78750948360693e-06 | 19905896596.7403
3441 | -3.82839509931361 | 20.109862749992
(4 rows)

Regards,
Dean

[1] https://github.com/postgres/postgres/commit/e954a727f0