Methods used to fit curves (as in linear or non-linear regression) to data.

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32 views

Fit a Gaussian to data with R with optim and nls

I want to fit a Gaussian to the following data: ...
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1answer
32 views

Likelihood between two functions

I have a function $f(x)$ describing a physical process, and a function $g(x)$ that tries to approximate it. I can clearly see by eye when the two functions are close enough, but I would like a ...
3
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2answers
222 views

Fitting a smoothed curve to a noisy data

I have a variable with sales data over time. It is very noisy at a disaggregate level but if you look at it as a whole, you can see a smoothing curve that follows a polynomial pattern. Is there a way ...
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12 views

Fit tail to monotonically decreasing data

I am trying to fit several distributions to monotonically decreasing data, and pick the one that fit the best based on several criteria, e.g. mle estimate. I am able to do this by fitting a curve to ...
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1answer
30 views

Construct function from integral values

From measurements (only) the values $a_i =\int_{x_i}^{x_{i+1}} f(x) dx$ for some sequence of (equispaced) $x_i$ are known about a non-negative function $f$. What would be techniques to find a ...
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8 views

Combining the results of 4 fits performed on 4 different dataset

I have 4 dataset which are independent measurement of the same physical quantity. I have fitted each dataset with a certain model, as a result of the fit I estimated one parameter with its uncertaity (...
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6 views

How to take dataset uncertainty into account in distribution fitting?

If we have a dataset like x=(3,4,2,1,4,...,5), we have classic methods (method of moments, maximum likelihood method, etc) to fit a distribution. However, in certain real life cases, we can have ...
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42 views

4th parameter of Boltzmann sigmoid must be greater than .9 in R

I'm trying to fit a 4 parameter boltzmann sigmoid and get an error: "Error in nls(y ~ a0 + (a1 - a0)/(1 + exp((a2 - x)/a3)), start = list(a0 = max(y), : singular gradient" I have figured out that ...
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3answers
111 views

Is there a formula for an s-shaped curve with domain and range [0,1]

Basically I want to convert similarity measures into weights which are used as predictors. The similarities will be on [0,1], and I will restrict the weights to also be on [0,1]. I'd like a ...
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0answers
45 views

Polynomial fit based on the addition of two least squares regressions

I'm wondering if there is a way to retrieve analytically the coefficient for a polynomial fit, based on a least-squares regression coming from two independent sources. Let me explain the context for ...
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31 views

Fit a curve to data with positive and negative peaks

I have some data from a finite element electromagnetic simulation, and I'd like to fit a curve to it (to allow me to scale the data without numerical artefacts). It goes to zero at plus/minus infinity ...
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28 views

How to detect the inflection point or the change point in a Q-Q plot?

Following are two QQplot. Both of them has an inflection point, which can be found easily by human eyes. However, I'm not sure whether there is a robust statistics way to find it.. Does anyone have ...
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58 views

How to improve a bad long-term forecasting of time series in common case

I have two time series $d_t(t)$, $d_c(t)$, where I'm modelling charge as a function of time. Lengths of time series, $N$ are equal to $101$ data points. For the $d_t(t)$ (test sample, short-term) the ...
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13 views

Powerlaw fitting with zeroes. Is this not the case?

As a result of a computation process which I cannot describe due to lack of time, I have obtained two datasets that I will simply call X and ...
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0answers
15 views

How to aggregate many simulation runs for curve-fitting?

I have results from about 200 runs of a simulation model. The results contain a stochastic response variable which I want to approximate with a curve-fitting approach. So far, I have opted for ...
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3answers
252 views

Pattern detection in scatter plot

Below is a scatter plot (capped at $10k) representing the average donation a project receives vs the word count of the funding request essay for all projects represented in the open Donors Choose Data....
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14 views

Polynomial curve fitting for temperature prediction

First of all, I would like to say that I know very little about statistics. I need to make a C# application to predict three days weather for school project and need some model and have been exploring ...
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0answers
14 views

A quantity is normally distributed with a mean of $t|y(x,\mathbf{w})$. [duplicate]

Let $y = \displaystyle\sum_{i=0}^Nw_ix^i$ be a polynomial fit curve. In this question, we are looking at this curve from a probabilistic perspective, as Bishop says, towards a full Bayesian treatment. ...
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1answer
77 views

Algorithm for weather prediction

I am trying to build a weather prediction app using c#. I am not a stats major and i am trying to understand which simple algorithm can be used to predict temperature and rain fall. I have gathered ...
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1answer
19 views

Justification by enhancement of $R^2$

Is (great) enhancement of $R^2$ sufficient to justify the use of another model ? other desciptives variables ?
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4answers
103 views

Looking for function to fit sigmoid-like curve

I'm looking for a function to fit sigmoid-like curves, from experimental data points. The model (the function) doesn't matter, it doesn't have to be physically relevant, I just want to be able to ...
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0answers
4 views

Interpolating data with errors (limited model knowledge)

I have data which I know follows a function $y = f(x)$ such that it is quadratic i.e. $y =\alpha x^2$ for some $\alpha$ when $x\rightarrow 0$ and $y = \beta x$ for large $x$. The data itself has ...
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1answer
167 views

Difference between non-linear curve fitting and interpolation

I understand the difference between linear curve fitting and interpolation. In interpolation, the targeted function should pass through all given data points whereas in linear curve fitting we find ...
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25 views

optim() convergence in fitting gamma distribution to separate peaks of time series data

Trying to fit gamma distribution to each separate peak of time series data (chromatography). As a peak i take local minimum-maximum-minimum part of the data each time. Since the peaks values do not ...
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24 views

Visualizing 3-D fit

I have two independent variables, call them X and Y, and I have to fit a dependent variable Z = f(X,Y) somehow. In an experiment, the experimentalist measured Z as a function of X, and another ...
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14 views

Trendline for data with two phases

I'd like to know how to fit a curve to a set of data that has two phases. For the below data I've tried using a third order polynomial, but I think that's overfitting the data and I've tried using ...
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32 views

How to fit a path through a dynamic, 3D point cloud?

I have a cable I am dropping from moving vehicle onto the ground. Using a camera system I estimate the location where the rope touches the ground in realtime. Movement of the vehicle and inaccuracy in ...
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20 views

Compare R Square values of different curve fitting

I have four independent samples (e.g. time vs. weight). I have used to two different methods to curve fit each sample: 1). log transforming weight (linear-log) and fit with linear regression; and 2). ...
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1answer
38 views

Linear Regression to detect between a linear and non-linear trend

I have measured the area of spread of a number of plants through time. I'm interested in trying to ascertain whether a linear or a non-linear relationship (i.e. quadratic) best represents the increase ...
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1answer
30 views

Curve : should I use the mean or all values?

In my experiments, I measure glycemiae at 7 different times to then draw a curve with R or Excel. For more precision, I duplicate my measures, so for each time I have 2 glycemiae. For now, curves ...
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33 views

Useful references to learn the essentials of curve fitting and its application?

I know this question might be a bit too broad, but I am looking for some pointers for self-study. I am given a set of data for which I have to identify the trends, and potentially come up with some ...
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13 views

Best-fit plane for a set of points

I have a set of 3D points, ie: $P\{(x_1, y_1, z_1), ..., (x_N, y_N, z_N)\}$. Each point in the set is a stellar object, and the $(x,y,z)$ system is defined from their equatorial coordinates and ...
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1answer
57 views

How to determine when the difference between two goodness of fit values is significant?

I have a data series that I'm trying to fit to a model. I'm trying several types of models (exponential, linear, logarithmic). In order to assess which one it fits best, I use a Residual Sum of ...
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63 views

Calculate Confidence (Error) Bands for Chi Square fit with errors using Iminuit

I want to fit some data with errors to a polynomial, say $y(x)=a+bx$. I made a $\chi^2$-fit using Iminuit but now I want to calculate the error bands ( 68,3% Confidence Bands). What is the fastest way ...
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4answers
388 views

What type of regression will improve the prediction for these data?

I'm quite new to regression problems in general. I have a simple data with 1 feature. I am trying to fit a regression model so that I can predict on new data set. So far, I tried to fit a linear ...
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31 views

How to improve the model of a fit to a sinus modulated sinus

I am trying to determine the amplitude of a sinus modulated sinus as accurate as possible. My sampling frequency is sufficently high and I am currently using a LSQ fit. The entire model looks as ...
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250 views

Anscombe-like datasets with the same box and whiskers plot (mean/std/median/MAD/min/max)

EDIT: As this question has been inflated, a summary: finding different meaningful and interpretable datasets with the same mixed statistics (mean, median, midrange and their associated dispersions, ...
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15 views

combining two linear fits

I have two linear fits, in this case taken from two calibrations of an instrument, one before and one after a field project. For the two linear fits I have the covariance matrix, but not the original ...
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15 views

How to find deviations in a signal?

I have a sinusoidal wave data with a noise in it. I know the details of the sinusoidal wave (Amplitude, frequency, Phase, bias). I am trying to find out the exact time and the duration for which the ...
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38 views

Curve shape estimation based on reference curves [closed]

I have a set of exponential curves $ ae^{bx} $ that represent the speed-power curve for a given vehicle (for a specific speed you need to use y amount of power). And given a point $ (speed, power) $ ...
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0answers
47 views

How does a curve fit accuracy depend on the number of points?

The accuracy of a curve fit must increase with the number of points (perhaps like sqrt(N)), but I haven't found an equation for it. Trying estimate accuracy of a 2nd order poly fit. Thanks.
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37 views

Averaging Cumulative Distribution Function

I have several (x,y) datasets which form various CDF curves. These are generated by cross-validating models built with different parameters. For example: ...
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21 views

How to modify a curve so that it reference another curve

Let's say we have a curve A with 50 time points (max = 60, min = 1). One way I can do is to standardize the values of the curve and make the range become [0,1] instead of [1,60]. However, I have ...
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2answers
118 views

how to fit pdf of known form to data

I have a set $X$ of 1000 data points. I know the PDF has a certain form, but there are two constant parameters for which I need to derive values in order to bet fit the data. Is there an established ...
3
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2answers
215 views

What does negative R-squared mean?

Let's say I have some data, and then I fit the data with a model (a non-linear regression). Then I calculate the R-squared ($R^2$). When R-squared is negative, what does that mean? Does that mean my ...
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37 views

Curve fitting - accounting for variability caused by different initial conditions (Matlab)

I'd like to fit a Gaussian model (composed of 1 to 5 Gaussians) to 55 data points, and then repeat this process for >1000 more data sets, each having 55 data points. I'm interested in the fitted ...
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13 views

Compare two groups fitted with different models

I have two group means that "behave" in different ways. Group A increases and reaches a "plateau-like" value. Group B stays almost steady. I have used a polinomic fit (cubic) for group A and linear ...
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1answer
142 views

What do I fit to a heavily positively skewed histogram?

I have a data which has heavily positively skewed variables. My manager has told me to fit it some distributions (univariate). The problem is that for most of the data the mean is far closer to the ...
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14 views

Curve fitting and analytical solutions vs kernel density estimation and sampling

I have some data, and I want to find the expected value of the maximum of $n$ samples of this data. What of the following methods would typically get me the best results? Visually inspect the ...
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69 views

How to estimate a probability distribution

Suppose I want to estimate a probability distribution, is it common practice to simply fit a function to a frequency histogram? So in my work, I am training a classifier, the performance of which is ...