# Questions tagged [least-squares]

Questions about (linear or nonlinear) least-squares, an estimation method used in statistics, signal processing and elsewhere.

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### Fitting a line through intercept 0

I need to code a least squares routine to fit a line $$y = m*x$$ into a 2d set of points $$(x_i,y_i)$$ How can I find the regression line without an interceptor?
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### Least Squares Intersection between multiple line segments

I'm wondering how I would go about computing the 'best fitting' intersection between multiple line segments (or even better lines of bearing) using the least squares method. I understand how to use ...
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### Understanding the Gauss-Newton Method

I have successfully implemented the Gauss-Newton method to a simple nonlinear least-squares problem as shown in the Wikepedia page here. As I understand it, the method uses the derivative of the ...
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### Convexity of linear least squares if derivative of coefficients is added to objective

My math background is quasi non-existent, so please bear with me. Context: I am implementing a method for spectral unmixing called MCR-ALS (Multivariate Curve Resolution - Alternating Least Squares) ...
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### Showing Normal Equations as Linear System of Equations

[This is a practice problem] I watched tutorials on least square method and normal equations and understood them too. However, i am confused with this question: Measurement vals $p_0 = 0, p_1 = 2$,...
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### Linefitting to 6 dimensional points

I would like to find a line best-fitting an arbitrary set of input points in 6 dimensions. Is there an efficient algorithm to accomplish this. Does the usual linear least square approach work here?
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### How to do regularization onto a vector?

Assume that we have a vector $x(k)$ that contains noise. We don't know the noise. Now we want to do regularization onto $x(k)$ so it will become more...clear. Is that possible? I assuming that it ...
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### What method should I use if I want to find best fit for a matrix $B$ inside matrix $A$

Assume that we have a real matrix $A$ with the size $n,m$. Then we have a real matrix $B$ with the size $i,j$ where $i << n$ and $j << m$. In other words, $B$ is much smaller than $A$. ...
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### Hessian of least squares problem

Consider the least squares problem $f(x)=1/2*\Sigma_{i=1}^{m}{e_i(x)^2}$. For the gradient of $f(x)$, I could understand that it equals to: But I do not understand the calculation of Hessian: Where ...
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### Is β_0 unbiased and consistent?

I have the following equation $y_i=β_0+β_1 x_{1i}+β_2 x_{2i}+e_i √(exp⁡(x_{2i}))$ I found that theoretically $β_0$ should be unbiased because: Would this explanation be correct? That said I'm ...
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### Matrix algebra properties square of $Ax-b$

I have seen the least squares formula derived like this : $f(x) = ||Ax-b||_2^2 = \\ (Ax-b)^2 =\\ x^TA^TAx-2b^TAx+b^Tb\\ \nabla f(x) = 2A^TAx -2Ab = 0 => x=(A^TA)^{-1}A^Tb$ I'm trying to derive ...
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### Determine missing points of plotted curve.

I have a scientific study with charts as the one in the image. They made a curve to merge data from different studies and methods... using the equations in picture. I have access to the resulted ...
Assume $A\in \mathbb{R}^{t\times n}$ and $b\in \mathbb{R}^t$. How to solve the following optimization problem in $x\in \mathbb{R}^n$? \begin{array}{ll} \text{minimize} & \|Ax-b\|_2^2\\ \text{...
Given a set of points $\{(x_0,y_0),(x_1,y_1),...,(x_n,y_n)\}$ where $0\leq x_i < 1$ and where the $y_i$ are noisy what method can be used to find a smooth, monotonic, sigmoid-like function to ...