Explained sum of squares: Difference between revisions

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In linear algebra terms, we have <math>RSS = \|y - {\hat y}\|^2 </math>, <math> TSS = \|y - \bar y\|^2</math>, <math> ESS = \|{\hat y} - \bar y\|^2 </math>.
The proof can be simplified by noting that <math> y^T {\hat y} = {\hat y}^T y </math>. The proof is as follows:
:<math> {\hat y}^T {\hat y} =
y^T X (X^T X)^{-1} X^T X (X^T X)^{-1} X^T y = y^T X (X^T X)^{-1} X^T y = y^T {\hat y}^T y, </math>
 
Thus,