# 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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### 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 ...
820 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 ...
49 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 ...
1k 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. ...
73 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 ...
80 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 ...
76 views

### 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 ...
98 views

### 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 ...
41 views

### 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 ...
65 views

### Error curve does not oscillate in between reference points using Remez

Using the Remez algorithm, implemented using multi-precision library, in certain functions that I want to approximate, the error curve does not oscillate in between reference points, and so no roots ...
24 views

### 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 ...
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)...
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,...
45 views

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: $$\psi(t) = \sum_{i=1}... 0answers 188 views ### Oscillating convergence in my Resilient BackPropagation (RPROP) implementation I have implemented in matlab a neural network that uses rprop's algorithm to update its weights. Strangely the error on the training set does not converge to a local minimum, but oscillates. Here is ... 0answers 2k views ### Piecewise linear approximation of an experimental data curve. Knots position constrained I need to fit a curve, obtained from experimental data, with a piecewise linear model (4 knots and therefore 3 lines). I tried using the MATLAB function ... 0answers 60 views ### linear solution of curve fitting on multiple linear functions differing by a multiplier I am facing the following problem. I know nonlinear least squares can provide a solution but I am wondering if a linear way to solve this data fitting problem may exists. This is my input dataset: I'... 1answer 45 views ### Linearization of Remez algorithm rational case In the rational case, we are interested to find polynomials P(x) and Q(x) s.t. f(x_k)-P(x_k)/Q(x_k)=(-1)^kE for k=1,2,\ldots, N where N=deg(P)+deg(Q)+2 This can be rewritten as$$ (1)~~~~~~(...
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 ...