# Search results

• Users: longrob
• In Set Theory, Logic, Probability, Statistics
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1. ### Please convince me (OLS matrix derivation)

OK, here goes again. I think I fixed the LaTex problems: let \mathbf{A=X^{\textrm{T}}X} where \mathbf{A} is a n\times n square symmetric matrix with elements a_{ij}. \mathbf{\mathbf{\boldsymbol{\beta}}} is the n\times 1 column vector. Expanding out...
2. ### Please convince me (OLS matrix derivation)

Hi again I need to stick with the pure linear algebraic derivation at the moment, but thanks anyway. I may come back to you later on that, as I am also interested in the geometric interpretation. Anyway, I think I have solved it. Basically, it revolves around the "rule" that the derivative...
3. ### Please convince me (OLS matrix derivation)

Hi Bacle, thanks for your messages. I'm glad I'm not the only one who is a bit confused by it. For completeness and the benefit of others, I'll explain the setup so that it's not necessary to refer to the link I posted. We have y = XB + e where y is a n x 1 column vector of responses X is a...
4. ### Please convince me (OLS matrix derivation)

Excuse me: I meant "the 3rd term in the expression above" not "the 2nd term on the RHS".
5. ### Please convince me (OLS matrix derivation)

Hi and thanks for your reply. Could you take a look here: http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf On page 18/19 you see exactly what (I think) you are referring to in terms of the orthogonal projection. What I am referring to is on the bottom of page 19: "Differentiating with...
6. ### Please convince me (OLS matrix derivation)

Hi all In the derivation of the normal equations for Ordinary Least Squares estimates we have B (m x 1 column vector) and X (n x m matrix). Could someone please convince me that the derivative with respect to B of B'X'XB is 2X'XB Thanks ! LR
7. ### Probability density: change of variable

If x is a random variable uniformly continuously distributed on [0.1], and y=x^3, then y has the density: \frac{1}{3}y^{-2/3} on [0,1] But, if x has the same distribution, but on [-0.5, 0.5], there seems to be a problem because we have y^{-2/3} for negative values of y. This is overcome if we...
8. ### A textbook on probability and statistics

I like Probability and Random Processes, Third Edition, by Grimmett and Stirzacker, (Oxford University Press, 2001).