Linked Questions

4 votes
1 answer

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 ...
David Epstein's user avatar
2 votes
1 answer

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 ...
Dail's user avatar
  • 2,637
2 votes
0 answers

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: ...
KirkD_CO's user avatar
  • 1,118
2 votes
0 answers

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 ...
user3706794's user avatar
1 vote
0 answers

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 ...
Stu's user avatar
  • 249
1321 votes
27 answers

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 ...
claws's user avatar
  • 13.5k
7 votes
7 answers

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 ...
Sergey's user avatar
  • 193
14 votes
2 answers

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 ...
MaHo's user avatar
  • 391
9 votes
1 answer

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 ...
Suzy's user avatar
  • 93
6 votes
1 answer

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 ...
Thomas's user avatar
  • 163
3 votes
1 answer

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 ...
user90622's user avatar
3 votes
1 answer

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 ...
user19758's user avatar
  • 321
2 votes
1 answer

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 ...
user1205901 - Слава Україні's user avatar
2 votes
0 answers

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 ...
larry77's user avatar
  • 203
1 vote
0 answers

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 ...
Julián Alcántara's user avatar

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