Talk:Least squares

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Justifying derivation of general solution for linear least squares

I think the notation $Y$ here is a little confusing, because $Y$ makes it seem like it could be a matrix, when in fact it has to be a vector:

L(D,{\vec {\beta }})=||X{\vec {\beta }}-Y||^{2}=(X{\vec {\beta }}-Y)^{T}(X{\vec {\beta }}-Y)=Y^{T}Y-Y^{T}X{\vec {\beta }}-{\vec {\beta }}^{T}X^{T}Y+{\vec {\beta }}^{T}X^{T}X{\vec {\beta }}

I'd consider replacing $Y$ with ${\vec {y}}$ . — Preceding unsigned comment added by Fadmmatt (talk • contribs) 17:53, 26 July 2020 (UTC)[reply]

Moreover, this equation seems incorrect about the beta

=Y^{\mathsf {T}}Y-X^{\mathsf {T}}Y{\boldsymbol {\beta }}-X^{\mathsf {T}}Y{\boldsymbol {\beta }}+X^{\mathsf {T}}X{\boldsymbol {\beta }}^{2}

77.147.1.34 (talk) 22:31, 28 November 2024 (UTC)[reply]

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complex application

Would it be worthwhile to mention how the formula needs modification for complex values? We don't want the squared error to be negative. (When I used it, I had to work this out from first principles.) One could simply make the formula more general by adding conjugation bars where appropriate, and explain that this is redundant when all values are real. —Tamfang (talk) 05:56, 3 May 2024 (UTC)[reply]