Linear regression: degrees of freedom of SST, SSR, and RSS

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I'm trying to understand the concept of degrees of freedom in the specific case of the three quantities involved in a linear regression solution,

i.e. $SST=SSR+SSE, $

i.e. Total sum of squares = sum of squares due to regression + sum of squared errors,

i.e. $\sum(y_i-\bar y)^2=\sum(\hat y_i-\bar y)^2+\sum(y_i-\hat y_i)^2$.

I tried Wikipedia and thought I had understood why the first (SST) and the third (SSE) have (n-1) and (n-2) degrees of freedom respectively, but I could not make out why (SSR) has 1 degree of freedom. So maybe I did not understand degrees of freedom after all. Can someone explain?

Thank you!

Sources: http://en.wikipedia.org/wiki/Degrees_of_freedom_%28statistics%29 http://www.cs.rice.edu/~johnmc/comp528/lecture-notes/Lecture9.pdf