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Results tagged with total-least-squares
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user 28666
A technique to estimate parameters $\beta$ of the linear model $Y=X\beta$ when both $Y$ and $X$ are subject to measurement error. Includes Orthogonal and Deming regression as special cases.
21
votes
Accepted
Does a correlation matrix of two variables always have the same eigenvectors?
Algebraically, correlation matrix for two variables looks like that: $$\begin{pmatrix} 1 & \rho \\ \rho & 1 \end{pmatrix}.$$ Following the definition of an eigenvector, it is easy to verify that $(1, …
- 107k
10
votes
Accepted
Fitting a plane to a set of points in 3D using PCA
When you perform principal component analysis (PCA) on your 27 points in 3D, you first subtract the mean vector $\mathbf m$ and then obtain three eigenvectors $\mathbf e_1, \mathbf e_2, \mathbf e_3$ o …
- 107k
67
votes
Accepted
How to perform orthogonal regression (total least squares) via PCA?
Ordinary least squares vs. total least squares
Let's first consider the simplest case of only one predictor (independent) variable $x$. For simplicity, let both $x$ and $y$ be centered, i.e. intercep …
- 107k