Timeline for Least squares residuals
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 28, 2021 at 1:59 | comment | added | Adrià Luz | @Ejrionm Yes. I think that will also be the case even if $p=n$ (the saturated model), as long as $X$ is full rank. | |
| Sep 27, 2021 at 18:12 | comment | added | Ejrionm | @AdriàLuz thanks, I understand the reasoning, but I'd like to have some math intuition, so you're saying that in the case of $p>n$ we have $X \hat{\beta}_i = y_i$? | |
| Sep 27, 2021 at 17:04 | comment | added | Adrià Luz | @AdamO Makes perfect sense, thanks. | |
| Sep 27, 2021 at 16:56 | comment | added | AdamO | You actually need the rank of $X$ to be bigger than $n$ to guarantee perfect prediction. Otherwise, the span of $X$ may be less is required to express each $Y$ exactly as a linear combination of the rows of $X$. | |
| Sep 27, 2021 at 16:51 | comment | added | Adrià Luz | @AdamO I was thinking about the number of parameters being estimated here - so it'd be the dimension of $X$. Please let me know if that's not correct. | |
| Sep 27, 2021 at 16:49 | comment | added | AdamO | Is $p$ the dimension of $X$ or the rank? | |
| Sep 27, 2021 at 16:44 | history | answered | Adrià Luz | CC BY-SA 4.0 |