Questions tagged [regression]

Regression analysis is the process of measuring and establishing a relationship between a dependent variable and one or more independent variables.

Filter by
Sorted by
Tagged with
1
vote
1answer
41 views

Gnuplot: How can I fit a range of points (out of the entire data) to a function?

I have a set of data obtained for the I-V characteristics of an LED. ...
0
votes
1answer
18 views

Minimize squared error of linear function

Let $M$ be a $m \times n$ matrix, $x$ a $n$-vector, $y$ a $m$-vector, and $\|\cdot\|_2$ represent the $L_2$ norm (i.e., Euclidean norm). Given $M,y$, the goal is to find $x$ that minimizes the ...
1
vote
1answer
60 views

Correct weighting in least squares fitting

I am trying to fit some data points $d_i$ to a non-linear model function $m_i$, which depends on a number of fit parameters $f_k$ (I want to determine these) and also on some known, constant values $...
2
votes
2answers
107 views

What equation should I fit this set of data points to?

I have done an experiment Estimation of silver nitrate by potentiometric titration with standard KCl solution. A plot of $\dfrac{\Delta E}{\Delta V}$ versus Volume of KCl solution gives the ...
1
vote
0answers
34 views

fitting exponential versus exponential w/ power

I have two models which I would like to investigate for my data. One form is: \begin{equation} \label{one} f(r) = A e^{-B r} \end{equation} and the second is: \begin{equation} \label{two} g(r)...
2
votes
2answers
42 views

Fitting 2D mapping data from multiple measurements

Given a set of points in a plane, and series of measurements of the distances between those points, how would I go about generating a best-fit model of the position of the points? For example, given ...
0
votes
1answer
818 views

Numpy.polyfit with regularization

I am trying to use the numpy polyfit method to add regularization to my solution. My non-regularized solution is ...
0
votes
2answers
52 views

Finding parameters numerically

I suspect that a function $f(x,y)$ is of the form $f(x,y)=a(bx+c)^{dy+e}$. I have access to several values of $f(x,y)$. How do I proceed numerically to find the parameters $\{a,b,c,d,e\}$? By ...
0
votes
1answer
30 views

Propagation of error in fitting two sets of data to each other

I have two sets of experimental data: $\phi(t)$ and $I(t)$. In theory they are related to each other as: $\phi(t) = nI(t) $. By fitting these curves together I can find the value of $n$ (which is a ...
0
votes
2answers
59 views

will this methodology end up giving me a nonsense regression equation.

I'm wondering if this is a valid methodology to find the best regression equation for a given data set. User provides a rang of estimated value for some set of variables. Th algorithm uses the ...
1
vote
0answers
49 views

Update model parameter with new data, discarding old data

I have this dataset, and I am using y = (a * x^n) / (b + x^n) Hill function as the model, where a is the limit of the Hill curve,...
1
vote
1answer
271 views

Compressed sensing: $\ell_0$ “norm” vs $\ell_1$ norm

Suppose we have a very efficient way to perform $\ell_0$ "norm" compressed vs $\ell_1$ norm compressed sensing. Specifically, $\ell_0$ "norm" compressed sensing is $$\eqalign{ & \min \quad {x^T}...
11
votes
3answers
470 views

Fitting Implicit Surfaces to Oriented Point Sets

I have a question regarding quadric fit to a set of points and corresponding normals (or equivalently, tangents). Fitting quadric surfaces to point data is well explored. Some works are as follows: ...
1
vote
1answer
237 views

Data Analysis - Cooling Efficiency

I have a question as I am starting my dive into computational analysis. I have a large set of data (~2 months) which includes the room temperature, HVAC status (heat/cool/off) and the location of ...
1
vote
1answer
33 views

Parameter identification for regression model

Consider the following regression model : Y = AX + BU where the size of Y is $N \times n$, A is $N \times n$, X is $n \times n$, B is $N \times n$ and U is $n \times 1$. The matrices X,Y and U are ...
1
vote
0answers
43 views

Best way to to find fitting parameters for time series of decaying-growing oscillator type

I have discrete time series emerging from the numerical simulations. It means that the time series can be slightly noisy. The time series should "obey" to the following formula: $$ \psi(t) = \sum_{i=1}...
7
votes
1answer
205 views

Methods to Estimate Optimal Distance Measure for Multidimensional Data Set

My problem at hand pertains to choosing a distance measure for use in locally weighted regression. In my particular problem, I have a data set that is upwards of 10 dimensions, where the variables ...
1
vote
1answer
573 views

Curve fitting for oscillating data

This is my first question. I have the following data that I'd like to approximate as a parametric function: \begin{align} y = a + (bx_1 + cx_2 + dx_3 + ex_1x_2 + fx_1x_3 + gx_2x_3 + hx_1x_2x_3 + i)*(...
4
votes
0answers
75 views

Calculus of Variations with unknown cost function but some data

I have a problem that I've framed out in a particular way, but I don't know if I'm re-inventing the wheel here. Is there an existing literature base in this problem? Does it have a corresponding term ...
2
votes
1answer
1k views

Fitting a rectangle to a point set

I have an ordered list of (2d-)points that are forming a (not axis aligned) rectangle and I'd like to recover that rectangle. Approximations like a minimal enclosing rectangle can't be used so that I'...
0
votes
1answer
75 views

For finding the track of an object through space(3d) over time, what is the correct slope equation to use in the algorithm?

I am working on a program that tracks a flying object through space and predicts the future position of said object. I was given some equations to use, but some of them do not look right, mainly the ...
1
vote
1answer
414 views

Clever ways to update LU factorization for ridge regression

Ridge regression can be posed as minimizing the following objective function (over $x$): $$\frac{1}{2} \lVert Ax - b \lVert_2^2 ~+ \frac{\lambda}{2} \lVert x \lVert_2^2 $$ Which has a closed form ...
1
vote
2answers
2k views

Finding rate of convergence by curve fitting in Matlab

I have some data: number of nodes $N$ and error in energy norm corresponing to it. I have seen in some references that the rate of convergence is reported by $$\| u-u_h\| _E=CN^{\alpha} $$ How can ...
1
vote
0answers
156 views

Oscillating convergence in my Resilient BackPropagation (RPROP) implementation

I have implemented in matlab a neural network that uses rprop's algorithm to update its weights. Strangely the error on the training set does not converge to a local minimum, but oscillates. Here is ...
4
votes
1answer
232 views

Problems Implementing the Remez Algorithm

So first off: *** This code is not being used in production software. It is a personal project of mine, trying to understand approximation theory and advanced curve fitting. In other words, I'm ...
1
vote
2answers
311 views

Polynomial approximation

Is there any universal method to fill this matrix for any $n$ value: $\textbf{A} = \left[ \matrix{n & \sum x_i & \sum x_i^2 & \cdots & \sum x_i^n \cr \sum x_i & \sum ...
0
votes
1answer
489 views

Power series regression linear fit in VBA excel

I wrote a program that calculates the best fit in VBA excel for the following model $$ y_k=c_1x_k+c_0+c_{-1}(x_k)^{-1} $$ solving for the best fit parameters $c_1$, $c_0$, and $c_{-1}$. However I ...
1
vote
1answer
209 views

Constrained linear least squares matrix equation

It has been a while since I have done linear least squares, so forgive the simple question, but here goes: I am attempting to find the best fit coefficients, $\{c_i\}$, of a linear combination of ...
0
votes
1answer
2k views

How do I correctly multiply vectors and matrices in Python and MATLAB?

I have been trying for 2-3 days now to get L2 regularized logistric regression to work in Matlab (CVX) and Python(CVXPY) but no success. I am fairly new to convex optimization so I am quite frustrated....
0
votes
1answer
111 views

Can Box-Cox transformation be applied for data of this form?

I have data of the form: X Y 3.53 0 4.93 50 5.53 60 6.21 70 7.37 80 9.98 90 16.56 100 And I want to find out $n$ so that this can be ...
4
votes
0answers
625 views

Neural network performs worse when using more input variables

This question is based more on the theory of neural networks than my particular implementation. Therefore I will leave out my code unless requested. I'm working on a project in C# which can create ...
1
vote
1answer
114 views

What are good parametrizations of rational functions for response surface models?

For fitting a response surface model to a physical process, I have 3-4 relevant "signals", like a feature density, a signal based on a feature width, or a signal based on a distance to the next ...
1
vote
0answers
2k views

Piecewise linear approximation of an experimental data curve. Knots position constrained

I need to fit a curve, obtained from experimental data, with a piecewise linear model (4 knots and therefore 3 lines). I tried using the MATLAB function ...
2
votes
1answer
124 views

fitting a non-linear curve

I have an equation: $\ddot{x}+(\delta+\epsilon\cos{t})x=0$ known as the Mathieu equation.The $\delta-\epsilon$ parameter space of this equation looks something like The red lines in this diagram ...
8
votes
5answers
3k views

Seeking a free symbolic regression software

Now that Formulize / Eureqa started charging $2500 a year for using it and having crippled the trial version, does anyone know of any replacements that can do similar things like find an equation ...
1
vote
0answers
57 views

linear solution of curve fitting on multiple linear functions differing by a multiplier

I am facing the following problem. I know nonlinear least squares can provide a solution but I am wondering if a linear way to solve this data fitting problem may exists. This is my input dataset: I'...
6
votes
4answers
3k views

Surface fitting

I do not need a complete answer but just some advice. I have a sparse matrix of points in a volume. I know a surface passing by these points exists and this surface is mostly flat and relatively ...
3
votes
0answers
934 views

Polynomial Fitting with Least Squares using Numpy and Scipy

I am trying to fit data to a polynomial using Python - Numpy. The points, with lines sketched above them are as in the picture. I am trying to fit those points to a polynomial of 4. or 5. degree. ...
1
vote
1answer
145 views

what went wrong with my logistic regression implementation in c++?

I have implemented a simple logistic regression function with IRLS algorithm using the armadillo linear algebra libray ...
1
vote
1answer
72 views

Least Angle when $\textbf{A}^T\textbf{A}$ is singular

I'm teaching myself this regression stuff, so forgive me if this is a basic question. I can't seem to find a discussion of my particular problem. So I'm least-squares-ing this overdetermined system $\...
3
votes
0answers
72 views

Why not use this simpler variant of Stepwise Regression?

In stepwise regression, you step predictor by predictor, each time selecting the one with the greatest correlation with the measurement, subtracting greedily to leave a residual with no correlation to ...
4
votes
2answers
7k views

Tikhonov regularization in the non-negative least square - NNLS (python:scipy)

I am working on a project that I need to add a regularization into the NNLS algorithm. Is there a way to add the Tikhonov regularization into the NNLS implementation of scipy [1]? [2] talks about it, ...
4
votes
2answers
320 views

Can the Levenberg-Marquardt algorithm be used for minimization and not fitting

Can the Levenberg-Marquardt algorithm be used for minimization and not fitting? Usually we input the derivative of the function we want to fit in the minimizer. Now if I assume I have an objective ...
2
votes
1answer
727 views

Some questions about MINPACK usage and messages

I am trying to use the nonlinear fitting routines of MINPACK for fitting a rather complicated equation of state to a set of experimental data. A subset of the data is fitted fairly well to a ...
3
votes
1answer
191 views

How to detect specific behavior in time series?

I was not quite sure what the right SE for this was, so I posted this also here on DSP. Please tell me which one to remove :) Problem statement I have a few hundred unrelated time series, say $P_i(t)...
3
votes
0answers
66 views

Partitioning Data for Multiple Regression Lines

We're all familiar with traditional least-squares method for constructing a straight line through a set of data points. The question is: suppose I show you a scatter plot which clearly is suggestive ...
3
votes
2answers
66 views

Parameter Fitting: Need measure of data 'support' for a parameter solution

I am estimating parameters on a dataset that would, for the most part, result in a weakly constrained solution. The dataset however also contains a few more data points that make the solution well-...
8
votes
1answer
5k views

Fitting one set of points to another by a rigid motion

I'm not really sure how to explain this problem clearly, so please bear with me. I have a basis of 3 orthonormal unit vectors and a position, a standard 4x4 transform matrix in computer graphics. ...
3
votes
1answer
58 views

How to obtain the minimum set of variables required in a model to produce accurate estimation?

I have a system which I assume is linear. I have a matrix $A$ of which each row is a coefficient of a unknown variables in vector $x$. I have vector $B$ which contains the result of each $Ax$. ...
3
votes
3answers
1k views

Averaging scattered data

I have multiple sets of measured data that can easily be visualized using a scatter plot (red and black points in the figure). If my measurements were perfect, the red and black points should lie on a ...