# What type of analysis to choose for this data?

I am trying to create a model of refrigeration having the energy consumption and the temperature over time. So far, I've tried regression but fitting this data into linear model seems impossible. Another thing that I've tried is cross correlation but it's insignificant (around 0.11 at lag 0). I also clustered the data and for another fridge I was able to state that if the fridge is in 'idle mode' (e.g. not consuming electricity) the temperature goes above certain value. However, for this fridge, this doesn't work as the data seems pretty random. Here is a scatter plot of the data, the bigger the circle, the higher the frequency.

Any ideas what type of analysis can I use to derive insights from this? I would like to know if there is any correlation between the kW data and the temperature data. A new plot for the full duration that I have:

• Can you please explain, what do you mean by "frequency" here? Aug 21, 2015 at 10:47
• Do you have the full time series? Aug 21, 2015 at 11:16
• Ah, sorry, I didn't realize that it's unclear. I mean how often those values appear in the data set. So the small dots are values which appeared only once while the big ones are values which appeared multiple times. I have time series for 6 months, collected every 15 minutes so it's 4 measurements per hour. There are some missing values so I divided the data into chunks because of this. Aug 21, 2015 at 11:17
• What is the goal of the analysis? Which questions do you want to ask the data? Aug 21, 2015 at 12:51
• If there is any correlation between the kW data and the temperature data. Aug 21, 2015 at 13:00

You clearly have a bimodal (multimodal for the second) distribution:

• standby (on the left)
• cooling (on the right)

It does not seem that the temperature settings affects the power intake.

Most likely, the fridge operates "binary", i.e. if the temperature is too high it starts cooling, and when it is cool enough it stops cooling again. Typical operation, because it's better to operate the cooling engine at a well-defined power intake and speed; and use duration to control.

Look for a correlation between cooling duration and temperature setting instead. The unit you want to observe is Joules, not kW (note that Joules relate to kWh!). I'd expect a correlation with Joules (= effort), not with power. Consider the power consumption of an appliance to be a sequence of constanta (off/on, or off/low/high); and expect them to use the time to steer the total effort.

Consider your stove. It probably has 4-6 different power settings only. In order to boil water (or anything), you would turn it on (probably to the highest setting; limited by e.g. safety considerations) and then wait for the water to boil. If you want to measure how much energy your stove used, you need to use "watt * time" (yielding kWh or Joules), one value is useless without the other.

• +1 The idea of looking at duration is insightful and appealing.
– whuber
Aug 21, 2015 at 13:35
• Thank you. That seems as a very good suggestion for a start. However, if I expand the data into bigger period, I have this: rpubs.com/canar40/102389 which means 4 types of operation. I'm sorry, I should have uploaded this graph instead. I will try to look for patterns for 4 of them now. Aug 21, 2015 at 13:43
• Still, clearly no correlation with the temperature setting in that plot either. Aug 21, 2015 at 14:27
• Thank you for that! From my column with kWh gathered every 15 minutes, I took the difference (as it is simply metering data which adds up in time) and now I have proper consumption. However, I still can't find any correlation, even with the difference of my temperature data, ccf is 0.09 at lag 1. I am trying to exclude the defrost cycles now to see if something will change as the fridge does not use energy during that time but the temperature raises. I will be glad if you have any other suggestions! Aug 24, 2015 at 19:42
• If you look at a fixed time (e.g. 15 minutes) then you are again not taking duration into account. You need to aggregate durations, not split them into 15 minute chunks. Aug 24, 2015 at 20:53