Cannot understand why total SS＝explained SS+unexplained SS I cannot understand why total SS＝explained SS+unexplained SS because geometrically the sum of two small squares is not equal to a big square.
I wish someone could explain that to me. Thank you.

This question of mine has several answers that discuss the details why, but the gist is that, for a linear model (WITH AN INTERCEPT), the minimization of the residual sum of squares forces the explained and unexplained vectors to be orthogonal, and then the Pythagorean theorem applies to a right triangle. Then this post of mine gives the decomposition of the total sum of squares; in the language of that post, the orthogonality means that the $Other$ term equals zero. (That entire decomposition can be viewed as the law of cosines, where the $Other$ term corresponds to the term with the cosine in it, so zero when the vectors are orthogonal.)
