Skip to content

Update terms for ESS, TSS, and SSR to specify uncentered vs centered? #238

@mmcky

Description

@mmcky

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 #217 (comment)

Metadata

Metadata

Assignees

No one assigned

    Labels

    No labels
    No labels

    Type

    No type

    Projects

    No projects

    Milestone

    No milestone

    Relationships

    None yet

    Development

    No branches or pull requests

    Issue actions