Linear regression is probably one of the most widely used statistical techniques in all of econometrics/data science. There are a couple reasons for this; its relatively easy and intuitive to interpret the model output, it’s not computationally expensive… etc.
In order to properly utilize this technique there are a certain set of assumptions that must be satisfied. These assumptions are known as the Gauss-Markov assumptions of Multiple Linear Regression which are named after some old dudes, Friedrich Gauss and Andrey Markov. These assumptions are as follows:
- Linear in the parameters
- Random Sampling
- No Perfect collinearity
- Zero conditional mean - the expected value of u given x = 0
- Homoskedasticity
With it being one of the most widely used techniques, its shocking to see how many people in practice don’t even consider these assumptions when doing their modeling, and for those that do, how misinformed they are with the true meaning of them. I’ve read some of the craziest things on forums like reddit. I just wanted to quickly talk through some of these assumptions that I see some of the most egregious misunderstandings.
Linear in the parameters
This is probably this most misconstrued of all the assumptions, most likely due to the words “linear.” I often see people say you can only use this if the relationship you’re modeling is linear.