Tuesday, April 27, 2010

Update on previous post

My last post included a feeble attempt at showing that there is some correlation between price and water usage.  The connection, I believe, still stands but a helpful reader made a suggestion that greatly improves the interpretation of the data.  So I switched the x and y axes and tried some other types of regression and came up with a pretty good fit using a power function.  Here's the new graph:

I'll spare myself the embarrassment of trying to explain power functions, but the equation listed on the graph (above the R-squared value) describes the curve and indicates a non-linear relationship between price and consumption.  As might be expected, demand drops off rapidly when price increases initially, indicating greater sensitivity to price at the high end of water usage, then drops off more slowly when you get down towards 50 gpcd, which would mostly be indoor water use (less discretionary).  That seems to make sense to me.

Also, the most recent update from Circle of Blue includes the data shown on the map in their previous update in table form.  And provides sources for the data as well!  Ask and ye shall receive.  The article also discusses the alarming phenomena of falling demand and rising prices that seems prevalent among water utilities recently.  This is an unintended consequence of some of the more progressive rate-setting policies (like increasing block rates) and has been occurring for several years here in Tucson.  It could be largely avoided, most easily by returning to single or seasonal rates for water but that would have other, unwanted consequences.  So until the standard formulas for cost recovery in water rates are changed it will continue to be a fact of life in many cities.

Saturday, April 24, 2010

How strong is the connection between price and water use?

I get a weekly email with updates from the website Circle of Blue, that occasionally contains gems like this one that showed up recently. What I've really been impressed with on their site are some of the nifty things they do by combining data with mapping functions.*  So if you scroll down on the Circle of Blue page linked above you will see a Google map that has a bunch of data call out points on it. Click on any of those points and it will show you data on per capita residential water use and average costs for water in each of the cities shown.**

By way of background, I received an email from John Fleck last year where he asked if I knew of a source listing per capita water use that compared "apples to apples" - i.e. comparing only residential water use, not just taking some random total water use number and dividing it by population. This can be surprisingly hard to find.

So as I was looking at the water use data I got the idea that it might be interesting to try plotting the gpcd numbers against the average price numbers just to see how well they correlate. And this is what I came up with:

 If I remember my statistics, 0.3563 indicates pretty strong correlation, but obviously there are other factors present besides price.  You might notice that I pretty much cherry-picked the data I presented as well.  I tried to include data from Western cities that might have similar water use patterns so that price would be main variable being tested here.  Is the result fairly obvious - sure.  But that's often the point of statistics - to test something that appears obvious and try to figure out if it really is.

Oh, and there was one other nice bit of data in the call outs attached to the map - it says what type of rate structure each city uses.  I hope the Circle of Blue folks keep up the good work.

* My only quibble with data presented in this way is that they don't indicate a source for their numbers.  There's an email address for the person who put the graphic together, so I might have to email him and find out where he got all his data from and verify that it really is "apples to apples".

** The data for Fresno is pretty shocking, but when you consider that they charge a flat rate for water and I believe still don't meter most of their connections it seems pretty self-evident.  Also I was disappointed that there was no gpcd data for San Diego and Los Angeles - they're probably pretty tired of taking their lumps for residential water use.