Regressions everywhere you look

Is there anything more enjoyable than putting your feet up, opening Excel, gathering data, and running regressions? Of course not. Let's take a look at household energy consumption as a function of cooling degree days (CDD). Cooling degree days are calculated by subtracting 65 from a day's average temperature. For example, if the day's high is 90°F and the day's low is 70°F, the day's average is 80°F. Eighty minus 65 is 15 cooling degree days. There's a similar measure for heating degree days. This data is used for a variety of purposes, including weather futures (derivatives tied to temperature allow utilities to hedge exposure to fluctuating weather). Recent data has put Dallas, TX squarely in climate zone five, with around 3200 CDD and 1800 HDD annually. Here's a nice graph of the country by climate zone:

1. CDD less than 2000, HDD greater than 7000
   
2. CDD less than 2000, HDD between 5500 and 7000
   
3. CDD less than 2000, HDD between 4000 and 5499
   
4. CDD less than 2000, HDD fewer than 4000
   
5. CDD greater than 2000, HDD fewer than 4000
   

When you regress the last two years of my monthly electricity usage in kilowatt hours against cooling degree days (standardized to a 30-day month for consistency), a clear trendline emerges. In the summer time, the air conditioner accounts for up to 80% of my electric usage. Based on the R-squared, CDD does a better job at predicting energy consumption than just plain temperature. In this case, an exponential regression has the best fit with the data. This makes sense, since the temperature transfer from the environment into the house is larger when the temperature differential between the two objects is higher. Therefore, extremely hot days will take a disproportionately large amount of energy to keep cool. Of course there are other variables, such as cloud cover, wind speed, humidity, etc. but this is a good start. It will be interesting to see if the cellulose insulation and radiant barrier foil I added to the attic last fall will have a statistically significant impact on energy consumption this summer.


Our gas bill is larger in the winter. This time, a linear regression of heating degree days against gas consumption in thousand cubic feet had the best fit with the data.