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:

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


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*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.
