[S] This is more philo-statistical than S-Plus, but...

Wim Kimmerer (kimmerer@sfsu.edu)
Mon, 02 Mar 1998 11:58:56 -0800

I have a strange problem regarding interpretation of regression results,
explaining that interpretation to engineers and management types, and
having my explanation stick. If anybody has advice for me, I will happily
compile and share it for the s-news list.

In San Francisco Bay there are several aquatic species whose (log)
abundance varies positively and linearly with the log of freshwater flow
into the estuary. The log of outflow is an appropriate x variable for
several reasons not directly relevant here. The log of abundance is (in my
opinion) preferable because it does all the good things to the residuals
that one would hope (i.e., eliminates heteroscedasticity, makes the
residuals roughly normal) AND because it is biologically interpretable in
the context of populations changing multiplicatively (literally and

The positive relationships referred to above are apparently monotonic over
the range of historic flows, in some cases excluding extreme values from
1983 (and maybe 1998, we'll see). They are also linear over that range,
and there is nothing about any of them that suggests variation from
linearity; however, n is only 16-30 depending on species, as these are
annual values. I interpret that to mean that, if future conditions are
similar to past conditions (yeah, big if), an increment of flow of X% will
result in an increment of abundance of Y%, all else being equal.

The engineers who run the water agencies see things differently. They
assert that their ability to control flow is limited to a fairly narrow
range, and that the flow range for the above relationships goes well beyond
what they can control. Therefore they don't need to include that range,
only what they can control. Naturally, this being biological data and all,
within that range there is too much variability to see any relationship.

Is there any way past this conundrum? I tried a few analogies (e.g. height
vs. basketball-playing ability) without much success.

I would be very grateful for any help.

Dr. Wim Kimmerer
Romberg Tiburon Center
San Francisco State University
PO Box 855
Tiburon CA 94920
Ph. (415) 338-3515
Fax (415) 435-7120
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