Assumptions of Linear Regression

In assumption #2, it is said that the independent variables are not random. Does it mean that the coefficients are not random or what? Thanks

It essentially means that the x-variables are controlled in the analysis.

You may also see a little more technical jargon: the x-variables are assumed not to follow a random process.

A contrast to this is the dependent variable-- we assume it follows a random process. This is why we can predict correctly on average the value of Y, but individual observations have a random error component added to our prediction of Y. The independent variables are assumed to not follow this kind of process.

Edit: you can read up on a fixed effect versus a random effect model to learn more, but I’m fairly certain thats beyond the scope of the CBOK.

Note that we often violate that assumption.

For example, when we compute a stock’s beta, we do a regression of the stock’s returns versus the market’s returns. Market returns are random.

Randomness in this context also means that if I take multiple samples of a population, those samples appear to be very similar. If they were very different each time, then that variable was random. This makes sense because in a regression you want to discover a relation that holds in time or between peers. A random variable doesn’t have any relation with other variables rather than randomness, which is not useful for nothing.

Thanks gentlemen

My pleasure.