Linked Questions
18 questions linked to/from How to perform orthogonal regression (total least squares) via PCA?
4
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1
answer
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How to find straight line minimizing the sum of squares of Euclidean distances from the points? [duplicate]
I have recordings of intensities of two fluorescent antibodies on a 2d image $2^{10} \times 2^{10}$ pixels in size, giving me $2^{20}$ pairs of numbers.
What is the best way to find the best ...
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2
votes
1
answer
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prcomp() vs lm() results in R [duplicate]
I have a simple matrix:
[,1] [,2] [,3]
[1,] 1 2 3
[2,] 4 5 6
[3,] 7 8 9
[4,] 10 11 12
I have to calculate linear regression ...
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2
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0
answers
466
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Multiple orthogonal regression in R [duplicate]
I have a project in which I need to perform orthogonal regression in a multiple regression case. For the non-multiple case, I've found Teetor's R Cookbook suggests using principle components:
...
- 1,118
2
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0
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How do I get from the eigenvectors of the covariance matrix to the regression parameters? [duplicate]
I have a linear regression problem
$$ y = a x + b$$
with errors on $x$ and $y$ that are uncorrelated and unitary and I have to find $a$ and $b$. To do this, I want to use principal component ...
- 99
1
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0
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54
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Programming Multiple Variable PCA Ratios [duplicate]
I would like to generalize Paul Teetor's A Better Hedge Ratio, which uses prcomp() to determine the orthogonal regression ratio between two variables. I am hoping to generalize this to multiple ...
- 249
1321
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27
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908k
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Making sense of principal component analysis, eigenvectors & eigenvalues
In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues.
I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like ...
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7
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7
answers
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Are there useful applications of SVD that use only the smallest singular values?
In a number of singular value decomposition (SVD) applications, for example Latent Semantic Indexing, only the biggest singular values are used to make searches and calculate distances.
Are there ...
- 193
14
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2
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Does a correlation matrix of two variables always have the same eigenvectors?
I perform Principal Component Analysis using two variables that are standardized. This is done by applying a SVD on the correlation matrix of the concerned variates. However, the SVD gives me the same ...
- 391
9
votes
1
answer
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Fitting a plane to a set of points in 3D using PCA
I am trying to estimate a midplane of a 3D model using the midpoints of paired landmarks, in order to reconstruct missing data (midplane refers here to the middle/saggital plane of the cranium which ...
- 93
6
votes
1
answer
3k
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Nonlinear total least squares / Deming regression in R
I've been using nls() to fit a custom model to my data, but I don't like how the model is fitting and I would like to use an approach that minimizes residuals in ...
- 163
3
votes
1
answer
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Standard error of the intercept in orthogonal regression
I want to perform a univariate regression but with substantial measurement error in both $x$ and $y$. I therefore want to try orthogonal regression with R. The best answer to my question so far have ...
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3
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1
answer
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Total least squares with weights [duplicate]
I am looking for a way to perform weighted total least squares in R. I know one can use PCA for this as described nicely in the following post.
How to perform orthogonal regression (total least ...
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2
votes
1
answer
427
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Curve fitting in the presence of prior beliefs about the relationship between x and y
In the figure which follows each dot represents a game of a particular sport.
The x-axis represents the home team's margin of victory, and so around the top-right we can see a game where a home team ...
2
votes
0
answers
602
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Confidence/prediction intervals for total least squares regression
I am learning the ropes of total least squares regression and I found this thread How to perform orthogonal regression (total least squares) via PCA? where the answer by @amoeba, together with some R ...
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1
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0
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Introductory references about total least squares
I am an engineering student and I've been recently told about the Total Least Square (TLS) method. I am interested in applying it to topographic measurements and in comparing the results with the ...
