Why is the SSE <= SST?

Question

I can think of a regression line producing a larger sum of squared errors (SSE) than the total sum of squares (SST). I read that should not be possible, how come?

My understanding is that the regression line is just a linear model, so if this model or line where above the data points it would result in a large SSE, in contrast the SST would be smaller.

Answer 1

The regression line is by definition the line $\hat y = ax + b$ that minimizes the SSE. On the other hand, the SST is the SSE resulting from the line $y = \bar y$.

By this definition, we see that we must always have SSE $\leq$ SST.