We're learning about multi regression in the current module of my statistics course, and the instructor noted that the sum of square errors (SSE) of a full model such as the one below:
is going to be smaller than the SSE for any reduced model, such as the one below (which we obtain under the assumption that $\beta_1=0$):
I'm having trouble understanding why this is true. If SSE is defined as:
Shouldn't the full model's SSE be bigger because it has more terms?