Was reviewing my notes the other day and suddenly I noticed something which has been on my mind.

The sample variance of a variable X is given as:

where we then adjust for the degrees of freedom by dividing by n-1.

However in linear regression the total variance (SST - Total sum of squares) in the dependent variable is given as:

While both are calculations of the variance for a variable, why is the former divided by n-1 while the latter is not given that for the latter we also have a sample that allows us to calculate the total variance? Am I missing something here?

Thanks