Timeline for Distribution of linear regression coefficients
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2023 at 2:27 | comment | added | profPlum | @WavesWashSands how did you get that: 𝑉𝑎𝑟(𝛽̂)=𝑉𝑎𝑟((𝐗^𝑇𝐗)^{−1}𝐗^𝑇𝐘)=(𝐗^𝑇𝐗)^{−1}𝐗^𝑇𝑉𝑎𝑟(𝑌)𝐗(𝐗^𝑇𝐗)^{−1} This could be a stupid question but I'm not sure what identities you used here? | |
| Jan 23, 2023 at 16:45 | comment | added | Julien | Does thoses first formulas hold for logisitic regression? (The ones until $Var(\pmb{\hat{\beta}}) = \sigma^2(\mathbf{X}^T \mathbf{X})^{-1}$) | |
| Jun 9, 2021 at 20:37 | comment | added | Brian | In response to one of the comments, the reason for "The response vector 𝐘 is multivariate normal, so 𝛽̂ is normal as well" is that $\beta$ is a linear function of Y. A linear transformation of a normal distribution is also normal. | |
| Dec 11, 2020 at 12:00 | comment | added | JRC | Good explanation @WavesWashSands ! | |
| Oct 5, 2019 at 0:17 | comment | added | WavesWashSands | @curious_dan Beta hat (not beta, I suppose it's a SE formatting issue) is a linear function on a multivariate normal vector. | |
| Oct 3, 2019 at 18:08 | comment | added | curious_dan | Can someone provide justification for this part of the proof: "The response vector 𝐘 is multivariate normal, so 𝛽̂ is normal as well" ? | |
| Jun 18, 2017 at 14:06 | vote | accept | Pieter Verschaffelt | ||
| Jun 18, 2017 at 14:06 | comment | added | Pieter Verschaffelt | I did indeed use the wrong X. Thank you for the very good explanation and clarification. I do understand what's happening now :) | |
| Jun 18, 2017 at 13:50 | history | edited | WavesWashSands | CC BY-SA 3.0 |
added 543 characters in body
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| Jun 18, 2017 at 13:41 | history | answered | WavesWashSands | CC BY-SA 3.0 |