# Questions tagged [regression]

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

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### biexponential fits where exponents are very similar to each other but different than best monoexponential fit

I have some data which consists of an exponential process in time convolved with a gating function. I am fitting the underlying exponential using the least squares method. (I also have experimental ...
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### How to model data that is repeated over time within the same group, from which outcome variable is categorical and explanatory variables are linked?

I have 1 dependent variable that is categorical. And I have 3 explanatory variables, the two continuous variables are likely interrelated and the 1 categorical variable is not interlinked. The sample ...
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### Remez algorithm convergence

I have implemented the Remez algorithm in Python where all calculations were done with the Python mpmath library. I have noticed that sometimes the $|E_{max}|$ and $|E_{min}|$ do not monotonically ...
48 views

### Comparing custom linear regression solver to SciPy equivalent in Python

From a given data set, I set out to complete a task which is below Fit the data of the previous exercise to fit Eq. (8.18) using the SciPy function ...
58 views

### Least-squares fit of explicit parabolic sheet to data points

For a given set of data points $$\{(x_i, y_i, z_i)\}$$ there exists some $$f_{ABC}(x,y)=Ax^2+Bxy+Cy^2$$ that minimizes $$\sum_i(f_{ABC}(x_i,y_i)-z_i)^2$$ $A$, $B$, and $C$ can be found quickly ...
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### Using linear regression to find the ideal point given a set of trajectory's data

I have a set of points in 2D obtained from a pendular movement with some noise. I want to determine where is equilibrium point ($x_0$, $y_0$) from which the rope is fixed. There are at least two ...
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### Proving convexity of Frobenius norm and correlation function formulations of an optimization problem

I have been working on formulating my requirements in the form of an optimization problem in a multi-output regression setting. Firstly, I would like to make the variables I used in the problem and ...
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### Good 3D surface fits for multiscale oscillatory surfaces

I have a 3D surface in $x$, $y$, and $z$. where $z$ is a function of $x$ and $y$ and my points are on a structured grid in $x$ and $y$. My function $z$ is highly oscillatory and irregular with ...
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### Efficient inversion of multidimensional non linear function

I have a function $f:x\mapsto \vec{y}$ with $x \in [0,1]$ and $\vec{y}=(y_1,...,y_n) \in \mathbb{R}^n$. $n$ is a small integer e.g. $n=8$. Each of the component functions in $y_i(x)$ "oscilate" up and ...
1 vote
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### Fitting a multivariate PDE (using Java)

I'm doing simulations of 2 coupled PDE's with Comsol Multiphysics. I want to fit some data (using the Application method, whose language is Java) to those simulations. In order to answer my question ...
1 vote
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### Spline regularization

I am fitting some B-splines to data, but the data has a "gap" region where the spline is less constrained by the data. I want to devise a regularization scheme to help prevent the spline from ...
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### 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. ...
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### 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
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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 $... 2 votes 2 answers 656 views ### What equation should I fit this set of data points to? I have done an experiment Estimation of silver nitrate by potentiometric titration with standard KCl solution. A plot of$\dfrac{\Delta E}{\Delta V}$versus Volume of KCl solution gives the ... 1 vote 0 answers 37 views ### fitting exponential versus exponential w/ power I have two models which I would like to investigate for my data. One form is: \begin{equation} \label{one} f(r) = A e^{-B r} \end{equation} and the second is: \begin{equation} \label{two} g(r)... 2 votes 2 answers 92 views ### Fitting 2D mapping data from multiple measurements Given a set of points in a plane, and series of measurements of the distances between those points, how would I go about generating a best-fit model of the position of the points? For example, given ... 0 votes 1 answer 3k views ### Numpy.polyfit with regularization I am trying to use the numpy polyfit method to add regularization to my solution. My non-regularized solution is ... 0 votes 2 answers 66 views ### Finding parameters numerically I suspect that a function$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\}$? By ... 0 votes 1 answer 37 views ### Propagation of error in fitting two sets of data to each other I have two sets of experimental data:$\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$(which is a ... 0 votes 2 answers 63 views ### will this methodology end up giving me a nonsense regression equation. I'm wondering if this is a valid methodology to find the best regression equation for a given data set. User provides a rang of estimated value for some set of variables. Th algorithm uses the ... 1 vote 0 answers 53 views ### Update model parameter with new data, discarding old data I have this dataset, and I am using y = (a * x^n) / (b + x^n) Hill function as the model, where a is the limit of the Hill curve,... 1 vote 1 answer 334 views ### Compressed sensing:$\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}... 15 votes 3 answers 1k 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 1 answer 243 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 1 answer 47 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 0 answers 49 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 1 answer 212 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 1 answer 2k 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 0 answers 80 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 1 answer 2k 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 1 answer 80 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 ... 3 votes 1 answer 935 views ### Clever ways to update LU factorization for ridge regression [duplicate] Ridge regression can be posed as minimizing the following objective function (overx$): $$\frac{1}{2} \lVert Ax - b \lVert_2^2 ~+ \frac{\lambda}{2} \lVert x \lVert_2^2$$ Which has a closed form ... 1 vote 2 answers 3k 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 0 answers 215 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 ... 7 votes 1 answer 834 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 2 answers 339 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 ...
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 ...
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 ...