The place we use linear regression with interactions to benchmark the efficiency of my new central heating boiler in an power disaster
With the battle raging in Jap Europe, one of many side-effects is skyrocketing power costs. My gasoline costs simply quadrupled because the begin of the yr, so like nerd sort knowledge scientist I began to review my power utilization knowledge to assuage my worries. Fortunately, my power supplier allowed me to obtain day by day gasoline utilization knowledge for the previous few years. One of many first issues that struck me was that our gasoline utilization this yr was decrease than I anticipated based mostly on the earlier years. One of many prime suspects that would trigger this was the set up of a brand new central heating boiler on the finish of april 2022, as it’s the solely equipment that makes use of gasoline.
On this article we discover my power knowledge, and construct a regression mannequin together with interactions that quantifies simply how a lot my new central heating boiler influences my gasoline utilization.
Word: This text will also be learn on github, together with all of the code.
The first knowledge supply is the web site of my power provider, Eneco. From their on-line system they permit me to obtain an Excel sheet with day by day power utilization. Word that I normalised my utilization knowledge (min-max scaled) to guard my knowledge privateness. As well as, I additionally downloaded temperature knowledge for a climate station close by as I think the gasoline utilization will rely strongly on outdoors temperature. The next code reads the info and merges each datasets based mostly on date:
the place the dots are the day by day gasoline utilization values, and the road the weekly common. This clearly exhibits the yearly development in gasoline utilization with excessive utilization in winter and decrease in summer season. A really putting characteristic is that the day by day values accumulate on horizontal strains. That is as a result of gasoline utilization being reported in integer increments, successfully rounding the values all the way down to the bottom closest integer. To mitigate this integer impact we resample the entire dataset to weekly summed gasoline utilization and weekly averaged temperatures. Utilizing this resampled knowledge we create a plot that visualises the connection of temperature to gasoline utilization:
Which clearly exhibits that there’s a very sturdy correlation between temperature and gasoline utilization. Utilizing this impact as a baseline, we are able to now attempt to mannequin the impact of changing out central heating boiler.
Our first step in benchmarking the boiler is to create a collection boxplots of gasoline utilization per 30 days. As well as, for the few months submit set up of the brand new boiler we add separate containers:
Which exhibits us the primary trace that the brand new boiler makes use of much less gasoline with the submit set up months (Could-Sept, cyan containers) displaying a lot decrease gasoline utilization. The subsequent step is the recreate our temperature versus gasoline utilization plot for each pre and submit set up knowledge:
This confirms our earlier commentary: gasoline utilization is decrease and the impact appears to scale with temperature because the slope of the regression line is considerably decrease. Nevertheless, the submit set up knowledge remains to be very restricted and never a number of weeks are included the place our heating was triggered due to the chilly. However given the very excessive gasoline costs at present, this supplies me with some hope that we are able to get by the winter with much less gasoline than the earlier winter.
To quantify the impact we create a regression mannequin utilizing statsmodels’ components interface. Word we can not merely embrace our two variables within the components like this `T_gem + C(post_install)`, as it will solely enable the intercept to be completely different between the strains. That is clearly not what we wish given the results of the plot above, we wish various slopes submit and pre set up. The answer is to make use of interactions, i.e. telling the regression mannequin the connection between `T_gem` and `gas_usage` varies based mostly on `C(post_install)`. Within the components you possibly can specify this utilizing a `*`: `T_gem * C(post_install)`. This implies the connection (slope) between `gas_usage` and `T_gem` will be completely different for the 2 values of `C(post_install)`, ensuing within the two strains within the plot above. Operating the code yields:
the place the coefficients should be interpreted as:
- `Intercept` the (anonimized) gasoline utilization at zero levels centigrade
- `C(post_install)[T.True]` at zero levels, the brand new boiler makes use of 1.73 much less gasoline
- `T_gem` for every diploma improve in temperature from 0 the gasoline utilization drops 0.15
- `T_gem:C(post_install)[T.True]` for every diploma improve in temperature the good thing about the brand new boiler when it comes to gasoline utilization drops by 0.09
The added impact of those coefficients is what we count on: the brand new boiler makes use of much less gasoline however the absolute impact turns into much less sturdy with increased temperatures. Which is the very same impact that two completely different slopes have.
For the restricted dataset I’ve after set up of my new boiler, issues are trying good. It makes use of much less gasoline, and can hopefully considerably impression my utility invoice. There are nonetheless some limitations: the info submit set up is kind of restricted in comparison with the years price of pre set up knowledge, particularly as a result of no submit set up winter is included within the knowledge. This coming winter I’ll after all accumulate extra knowledge, which is able to present extra certainty. One potential disturbing issue could possibly be that we turned down our thermostat all the way down to 18 levels, virtually definitely impacting our gasoline utilization. However that is an fascinating matter to sort out in spring.
This text will also be learn on github, together with all of the code.
My identify is Paul Hiemstra, and I work as a instructor and knowledge scientist within the Netherlands. I’m a combination between a scientist and a software program engineer, and have a broad curiosity in every part associated to knowledge science. You’ll be able to comply with me right here on medium, or on LinkedIn.
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