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I think a more commonly seen definitions of (centered) TSS, ESS and SSR are given here where the decomposition only holds when
So, I think it might be clearer if we replace
Here are some more standard definitions:
* The **total sum of squares** is $:= \| y \|^2$.
* The **sum of squared residuals** is $:= \| \hat u \|^2$.
* The **explained sum of squares** is $:= \| \hat y \|^2$.
> TSS = ESS + SSR
with
Define:
* The (uncentered) **total sum of squares** (TSS) is $:= \| y \|^2$.
* The (uncentered) **sum of squared residuals** (SSR) is $:= \| \hat u \|^2$.
* The **explained sum of squares** (ESS) is $:= \| \hat y \|^2$.
We have the relationship:
$$
\text{TSS} = \text{ESS} + \text{SSR}
$$
```{note}
For the centered case, see [here](https://en.wikipedia.org/wiki/Explained_sum_of_squares).
```
Please let me know your thoughts on this!
Originally posted by @HumphreyYang in #217 (comment)
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