Above is the question from Kaplan, I’d like to why wouldn’t the return 3% if both beta and market cap are 0. I dont think its because of the error term as error terms are 0.
Tough to answer without seeing the full question, but my first reaction would be: how can we determine an expected return on equity for a company that has no equity (since it has a market cap of 0)?
How can marketcap be 0? You are investing in nothing?
Oh right make sense. Thank you!
The above posters are correct. Two quick things will help you with this in regression (and statistics):

avoid extrapolation if your sample does not contain values of 0 for all of those independent variables, you shouldn’t make an interpretation of the intercept when all the X’s = 0; If your x variables have a range of negative to positive, but you don’t observe EXACTLY 0, you can still make the interpretation because it’s within the relevant range in the sample, so observing

avoid nonsensical inference/interpretations: if it’s impossible or doesn’t make sense to have all set to zero simultaneously, then interpreting the intercept with all X = 0 is nonsensical.
So, you must both have observed zeros in your sample (or at least both sides of zero, say 4 to +5 for all variables of X) and it must make sense to have all predictors simultaneously zero in order for you to interpret the intercept.
* for number 1, the more strict would be that if you haven’t observed this particularly combination in one case, even though zero was observed individually for each variable (I.e. no one with all X =0) you should avoid the interpretation because this is hidden extrapolation