Finding p and t value in LinearRegression using sci-kit learn

Question

I found from here, a way to calculate p and f statistic using Sci-Kit Learn. But what I don't understand is,

1. Why is SSE divided by x.shape[0] - x.shape[1].
2. I may be wrong, But Isn't this component called the Degrees of Freedom, for which the formula is

n-k-1 where n:= No. of observed values, k:= no. of predictors