It’s been a week. I got quoted in Bloomberg again for some reason, talking about meme stocks again.
As I discussed in my previous post, the art of prediction is a dangerous game. It’s quite easy to fall prey to biases, especially given the natural optimism of humans and desire for explanation of pure randomness.
Let’s take a step back. What does prediction even mean?
Correlation and Confusion
Most echo the axiom “correlation does not imply causation” without really understanding what it means.
Correlation is simply the relationship between two variables. These can be logically related variables, and often are. We can construct a simple example of correlation looking at the relationship below between electricity bills and ambient temperature:
In this contrived example, we’re looking at the relationship between background temperature (measured in Celsius) and the monthly electrical bill (measured here in rupees). This shows a clear positive correlation — as temperature increases, so does the electrical bill. This intuitively makes sense — as the temperature rises, we expect people to put on their air conditioning, which will increase their electrical bill.
However, correlations can also be negative — an inverse relationship between two variables.
In the above, we can see a clear negative relationship between amount of missed classes and exam score. This makes sense also intuitively, given we expect the relationship between the two is causal — missing class means missing learning opportunities, which means likely poorer understanding of the material.
In both of the above examples, I made it easy for you by conflating correlation examples with causal examples. In the first — electricity bill versus temperature — the relationship is causal, mediated by a third variable — usage of the air conditioning unit. In this relationship, we can model causality between the two variables as such: