# Questions tagged [total-least-squares]

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.

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### How to handle nondifferentiable points of the objective function in the geometric circle fit?

We a given measured points in $(x_i,y_i) \in \mathbb{R}^2$, $i=1,..,n$. The geometric circle fit is the circle with center (a,b) and radius $r$ that minimizes the squared Euclidean distances between ...
1answer
25 views

### Errors only in variables model, and polynomial fitting

I have a bunch of data points $(x, y)$, and I know that they fit well to a model of the form $y = a + bx + c x^2$, with $a \approx 0.01, \ b \approx 1\ \textrm{and}\ c \lesssim 0.1$. I'd like to fit ...
1answer
55 views

### Use of ordinary least squares line in correlation analyses

I want to study and plot the correlation between two variables, X,Y. Both are measured, so they have comparable noise. Correlation (and not regression) is the correct analysis here. In a paper, I ...
0answers
50 views

### How to do Error in Variables regression with known standard errors

I need some help with EiV regression and comparison of two methods. I have used two different methods to estimate the size of the same population and would like to find out how good method 1 is ...
1answer
40 views

### Linear regression with normally distributed data and model with arbitrary covariance

Consider the linear regression problem $$(A+\Delta A)x = b + \Delta b.$$ If $\Delta A = 0$ and $\Delta b$ is identically and independently distributed, then ordinary least-squares gives a good (BLUE) ...
1answer
29 views

### Which is more correct to calculate least squares (errors) during nonlinear curve fitting, calculating after transformation or in the original form?

I am studying curve fitting and linear regression. I am supposed to find a and b in the equation $$P=ae^{bh}$$ so I transformed it to $$lnP=ln a +bh$$ then $$Y=c+bX$$ after that I solved it to ...
0answers
44 views

### Identifying an algorithm described as 'Tukey approach' for ignoring outliers?

MVTec's machine vision library Halcon has an operator fit_line_contour_xld for robustly fitting lines to 2D points. Here's the documentation entry for that operator:...
2answers
508 views

### Including model uncertainty in non-linear least squares minimization

The problem I have experimental data $Y$ with heteroscedastic and normally distributed uncertainties characterized by covariance matrix $C_{exp}$. I want to fit the data using model $F(X, \beta)$ ...
0answers
19 views

### Standardizing regression coefficients in the case of Total Least Squares Regression

So I know that there exits a method to standardize regression coefficients by simply multiplying them with the ratio of the standard deviations of the two variables. I'm wondering if this holds true ...
1answer
61 views

### Difference between estimating parameters for prediction and estimating parameters for their own sake

In a 1989 paper on orthogonal regression, Ammann and Van Ness write: An important caveat should be noted. The errors-variables-model is useful when the primary goal is to estimate the model ...
1answer
186 views

### Statistical library for orthogonal distance regression with a ridge penalty?

There are many libraries in R and python for doing orthogonal distance regression and for doing ridge regression separately. Is there one for doing them at the same time?
0answers
559 views

### Difference between “orthogonal distance regression” and “total least squares”

I'm trying to figure out the difference(s) between total least squares (TLS) and orthogonal distance regression (ODR). Both techniques are used when there is error in the dependent variable. Per this ...
0answers
39 views

### least absolute deviation version of deming [closed]

Based on what I know, deming minimizes the sum of square of perpendicular distance to the regression line. Is there a package in R that can run regression that minimize the sum of absolute value of ...
2answers
515 views

### Why my Deming Regression line change so much when switching variables? If they seem to be a linear relationship betwen them?

I am trying to fit a line that best predicts the production of energy Y given the speed of wind X, a typical Y = xm + b , using deming regression. I am looking for the slope and the intercept of that ...
1answer
38 views

### Correct way to fit a line in 3D (x-position vs y-position vs other quantity)

I have measured the position of light spots $(x,y)$ in an arbitrarily chosen basis and I compare that to some other measured quantity, say the brightness of each spot $B$. Now, in theory all the ...
1answer
253 views

### Deming regression prediction interval using jackknife resampling

I am trying to write a custom Deming function following the maths in Linnet (1993): https://www.ncbi.nlm.nih.gov/pubmed/2281234 Using jackknife resampling I calculate the standard error for the ...
1answer
329 views

### Standard error of coefficient estimates for model II regression

I'm working with time series data that has error in both the dependent and independent variables, so I'm analyzing each half hour of data with model II linear regression, specifically geometric mean ...
1answer
86 views

### Selecting appropriate likelihood during non-linear regression

When performing regression to fit a function, $f (x,{\bf \beta})$, to a set of observed data, $y_i(x_i)$, we are seeking to optimize the parameters, $\beta$, of the fitting function, to minimize some ...
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27 views

### Can total least squares be used to account for uncertainty due to measurement timing?

Suppose we have a dataset in which we wish to perform regression analysis, and where the response/dependent variable is a measurement at time T. But due to pragmatic sampling we do not have ...
1answer
54 views

### Regression to estimate parameters

I would like some suggestions to tackle the following problem. Given a system $y = X\beta$ where $y \in \mathcal{R}^m$, $X \in \mathcal{R}^{m \times n}$, $m\geq n$, and $\beta \in \mathcal{R}^n$, ...
1answer
199 views

### Orthogonal polynomials + cross validation: should subsetting be done prior or after constructing the orthogonal polynomials?

So, just to start... I've just learned of orthogonal polynomial regression today. I've gone through the master's-level linear models courses, and we did not cover that topic. I was always under the ...
2answers
847 views

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### How to calculate confidence/prediction bands for Deming regression

Revised question: My fundamental question seems to be: "I have data with error both in y and x. How do I estimate a value of true x so that y evaluated at that x will be distinguished from y(0) say, ...
1answer
403 views

### Is it possible to make a regression with known standard error on y

I want to compare estimate with standard error in function of a continuous variable and a categorial variable . Here an example of what my data look like. ...
2answers
4k views

### Is it possible to calculate R-squared on a total least squares regression?

I am using the Deming function provided by Terry T. on this archived r-help thread. I am comparing two methods, so I have data that look like this: ...