0
votes
1answer
24 views

Linear system of equations and multiple linear regression: Numerical solving

I am currently implementing a test procedure for data, namely a linear form of the Kramers-Kronig relations (paper here: http://jes.ecsdl.org/content/142/6/1885.abstract). This includes solving a ...
2
votes
0answers
29 views

Smallest set of Liner equations, which exactly fit a set of points

I have a set of 2-d points,(it can be of any arbitrary dimension n). I want to find the minimum set of straight lines(linear equations) which exactly passes through the given 2-d points (unlike ...
1
vote
0answers
356 views

Least Squares “analytic expression” for fitting a 2D quadratic function to measurements

I have n scattered elevation measurements: $ \{x_i,y_i,z_i\}_{i=1..n} $ that I want to fit a quadratic function to: $ z = ax^2 + by^2 + cxy + dx + ey + f$. The problem can be written as a vector ...
1
vote
0answers
270 views

What is the Moore-Penrose pseudoinverse for scaled linear regression?

The matrix equation for linear regression is: $$ \vec{y} = X\vec{\beta}+\vec{\epsilon} $$ The Least Square Error solution of this forms the normal equations: $$ ({\bf{X}}^T \bf{X}) \vec{\beta}= ...
2
votes
0answers
114 views

Orthonormal Matrix weighted regression

$Q$ is a rectangular matrix with orthonormal columns. A linear system composed of $$Qx= b$$ is really easy to solve as: $$Q'Q=I$$ hence: $$x=Q'b$$ Given that $Q$ is orthonormal can this be used to ...
1
vote
1answer
174 views

QR factorization for ridge regression

I am solving an overdetermined system of equations: $$Ax= b$$ Using QR factorization, we can solve this system easily by posing it as: $$Rx= Q'b$$ I would like to regularize my estimate of $x$. I ...
0
votes
0answers
44 views

Derivative of $H$ with respect to $W$

I am trying to solve a generalized linear squares model with the following form: $\hat{Y}= X(X'\Omega^{-1}WX)^{-1}X'\Omega^{-1}WY $ $ H= X(X'\Omega^{-1}WX)^{-1}X'\Omega^{-1}W $ $ \Omega$ is the ...