QuantEcon / QuantEcon/lecture-python-advanced.myst
Update terms for ESS, TSS, and SSR to specify uncentered vs centered?
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Description
I think a more commonly seen definitions of (centered) TSS, ESS and SSR are given here where the decomposition only holds when $X$ includes intercept term.
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 https://github.com/QuantEcon/lecture-python-advanced.myst/pull/217#discussion_r2250749514
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Research direction
Locate the lecture text containing the displayed TSS, SSR, and ESS definitions, using the wording from this issue and the original discussion in pull request #217. Update the terminology as proposed, including the centered-case note, then verify that the rendered equations and note are correct.
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