Exactly how many parameters are in multiple linear regression? (some sources include sigma squared, some don't) I've read some resources such as my Introductory Econometrics textbook that state the model parameters are $B_{0}$, $B_{1}$, ..., $B_{p}$ where $p$ is the number of predictors in the model.
Other resources include $\sigma^{2}$ as well as one of the 'model parameters'.
Is there a reason for the discrepancy?

If you're trying to work out how many df to use in your t or F distribution, you need to count the mean-parameters and not the variance parameter.
If you need to work out how many parameters you have in a BIC or an AICc say, then you should be counting the variance parameter. (On the other hand, for AIC itself, it won't matter whether you do or not, since it will just shift everything by the same constant. Unless you're doing something fairly unusual like comparing models with different numbers of variance parameters; in the general case, include all the parameters.)
