Questions tagged [curve-fitting]

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

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13
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6answers
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What kind of curve (or model) should I fit to my percentage data?

I am trying to create a figure which shows the relationship between viral copies and genome coverage (GCC). This is what my data looks like: At first, I just plotted a linear regression but my ...
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0answers
37 views

Modelling the heat exchange between a steel cylinder and the surrounding medium [duplicate]

Massively refactoring my question after @user2974951 feedback below. I have a set of measurements (time, temperature) that correspond to a certain physical process. Both time and temperature ...
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22 views

Non-linear Least squares fitting in R [migrated]

I want to fit a curve to a set of 3 data points (1,65), (200,70), (800,75) in the form $y = \frac{ax}{b+x}$ Using the set of points I have this set of equations $a-65b = 65$ $200a-70b = 14000$ ...
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0answers
21 views

Straightforward explanation of Theil inequality statistic for curve fitting

I’ve come across a paper (here) that uses a “Thiel inequality statistic” (pages 9 and 10 of the supplementary information) to determine goodness of fit for a model with its training data. I was ...
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1answer
65 views

Improve monoexponential curve fitting in the initial portion

I've calculated the Tissue Volume and Tissue Mass from a Computed Tomography image of the lung of a given patient. The y-axis of the attached figure is Volume as a percentage of the total lung ...
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0answers
56 views

Simulate data for quadratically related variables

I'm looking to simulate a dataset with two variables (X,Y) where the relation between these variables is quadratic (inverted U shape) but not a perfect trend (meaning if Y is regressed onto the terms ...
3
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2answers
269 views

Curve fitting when data has a sharp initial slope and then tapers off

I have a dataset that I'm currently smoothing using a 6th order least-squares polynomial which models the initial sharp curve well but as the data tapers out some noise at the end causes a downwards ...
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0answers
13 views

Constraining parameters in NLS in R to be less than a value, or greater than a different value

The nls function in R comes with upper and lower arguments to specify the upper or lower ...
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0answers
25 views

Nonlinear fit in R only works with tightly restricting parameter bounds [duplicate]

I have a reproducible example here with an attempt to use nls to fit a nonlinear function: y = ax/(b+x) + c Even when I set the starting values to be a good, ...
2
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0answers
22 views

Detecting outliers in time series with fitting curve

I have a collection of time series that I know follow a particular type of non-linear functions. For each time series I use the LM algorithm to obtain a fitting curve. I have already checked that the ...
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1answer
34 views

Function to fit acid reaction curve

Data in the image below shows a variable DME reacting to the increase in acid concentration. It looks like it has a very fast increase from when the concentration is raised from 0 to 0.5 and then a ...
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0answers
41 views

Error while curve fitting in R [closed]

I need to fit the curve y = K + B*exp{ a*(log x) + b*(log x)^2 + c*(log x)^3 }. Where a, b, c, K, B are unknown parameters. I just have 5 data points which are, <...
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0answers
19 views

how to select training and testing data for interpolation in 100 instances data?

I would like to divide my data of only 100 instances into training and testing an use the training data to fit a curve(interpolate) and use the testing data to calculate the error at the interpolated ...
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2answers
89 views

R-Squared for a non linear curve

At the start, please forgive me if my question is too elementary. I am fitting a non-linear curve. Say a parabola. The data points I have are close to a parabola and the best output I get is a ...
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0answers
18 views

Scale and Translate a parabola to a golden distribution(which is also parabolic)

I have multiple image histograms(difference images) whose distribution is parabolic.I use least squares to do a quadratic fit .The questions is how do I scale and translate this parabola to a golden ...
2
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1answer
42 views

Estimate parameters of a normal knowing the density function

I have a matrix with 3 columns. The first column contains values of a variable $x_1 \in [-1,1]$. The second column contains values of a variable $x_2 \in [-1,1]$. The third column contains a variable $...
2
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0answers
40 views

Statistical significance of parameters in nonlinear model

I have historical data for mineral production in a specified region, from 1972 to 2014. I fitted the data to a model following a bell shape, in order to estimate the peak year and production. The ...
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1answer
34 views

How can I make a Kolmogorov-Smirnov test to check if my data distribution is exponential?

I made a histogram of my data, and the fitting line, but from some reason the fitting line doesn't fit to my graph. How can I make it fit to it? How can I check if my data distribution is exponential?...
2
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0answers
8 views

Uncertainty in calibration/curve-fitting parameters

Let me preface with saying I have an idea of a solution, but I am interested in other ones I am interested in the a way to quantify the uncertainty in a calibration/curve-fit parameter. For all ...
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0answers
28 views

Scaling and Transformation of histograms

Basically I have some histograms of images which I want to scale and transform so that if I apply a single threshold then I would get a constant alarm rate.How can I go about doing this.Below are 2 ...
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0answers
39 views

Matching a quadratic model to a linear model to give constant false alarm rate

I have a linear model which estimates the false alarm rate on different regions of an image on thresholding. Meaning the rate of false alarms is constant for all regions when a single threshold is ...
3
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1answer
43 views

How to fit a set of curves having some free and some shared parameters?

The problem I have a data set with 1 dependent and $N$ independent variables $x_1,\dots ,x_N$ (all real numbers), and need to fit a (nonlinear) function/curve $$ f_i(x_i; p_1,\dots ,p_{k_F}, r_1, \...
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0answers
22 views

Extend Best Line Fit methodology to a Grid

Sometimes, I'm provided with some data, a list of (x,y) points, and asked to determine a best-fit to some polynomial (or other function) that produces the inputs into the function that when chosen, ...
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1answer
29 views

How to extrapolate partial curve based on other complete curves?

I heat a room to a certain temperature. Then I let it cool over time. I measure the temperature at 6 intervals as it cools. I repeat this process for some other rooms. From this, I get a set of ...
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0answers
18 views

How to do curve fitting with data from measurements of experimental replicates (dose-response)?

Attached an image of a scatter plot based on sample data. I have tried searching the web but found only a video by Originlab doing concatenate fit. Tried looking for examples that use SPSS, Magicplot ...
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1answer
76 views

Get lower bounds and upper bounds of a curve

I have fit the wave data as below using Least Square optimization and used Root Mean square to calculate upper and lower bounds. I wanted to know is there any other alternative exists which gives a ...
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2answers
316 views

Fitting pmf of a scaled Poisson distribution and Python histogram plotting

I have a nuclei meanlife of $550\mu s$, for which I've taken the frequency(rate) to be $1/meanlife = 1818$. I then sampled randomly from a poisson distribution with that frequency, taking the ...
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2answers
63 views

Fitting curve to non-decreasing data

I have the below data. I want to fit a non-decreasing curve for this data. But, althouhg its grağh seems so regular, I couldn't find a suitable form of function. What kind of function may be suitable ...
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0answers
27 views

Working out a metric for the goodness of fit for 2D data in time

I have a dataset which I wish to optimise a fit for. The data might look something like I.e. orange is t=0, blue is t=1, and green is t=2. I wish to find a fit. I have a differential equation ...
3
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0answers
45 views

what is the best model that can be fitted onto a retention curve

I have a retention curve from activity data from customers which trends from 100% on day 1 down towards 0% over team in a curve. I need to fit a model to extrapolate this data past what data I have. ...
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35 views

Covariances and correlations in curve fitting

I have a set of data that I am trying to curve fit and I'm ultimately interested in the errors on my fit coefficients. I take my errors on each fit coefficient as the on-diagonal elements of the ...
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1answer
43 views

Approximate the data to a single curve

The question might be simple, but I am not able to find the answer. Hence I am asking here. I did search google but didn't get an answer. I have a continuous stream of data coming from an API in the ...
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1answer
54 views

Regression for curve fitting

For a curve generated from dataset points, split the curve into parts and obtain the best-fit degree of polynomial,coeffcients and the interval/range of the split through implementation in python.I am ...
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0answers
21 views

Area under the curve in smaller and uniform intervals?

I have 5 million individuals falling into 30 odd intervals, something like the below: 0: 9000 1-49: 8525 50-99: 7593 100-199: 7385 200-299: 4242 ... I would like to approximate the number of ...
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0answers
42 views

R - How can I fit the following data and get the equation describing them? [closed]

I have a following data-set: ...
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0answers
47 views

Confidence interval of fit parameter

First of all: I am quite new to statistics, so please don't tear me apart. ;-) I am currently trying to calculate a confidence interval for a fit of a curve to measured data points. I have done this ...
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1answer
46 views

Fitting a curve or raw transformation in a logistic regression

For my project, I am fitting a logistic regression to the some 'dummy' bank data. The head of the dataset looks like this ...
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1answer
52 views

method for predicting a curve

I have data on several curves. the data is of the form: curve_id x y and there are many x/y pairs for each curve and x is limited to some known range. overall, the curves look quite similar in ...
2
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0answers
90 views

How do I fit a cumulative Gaussian distribution in R? [closed]

I am trying to fit a cumulative Gaussian distribution function to my data, but I'm not sure how to do this. From what I understand, the fitting process tries to find the mean and standard deviation of ...
2
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1answer
21 views

Analyse variation between distribution curves according to factors

I have a set of continuous distributions representing the leaf area density found at different heights through a forest canopy. e.g. like that found in Whitehurst et al. (2013): For each of these ...
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0answers
29 views

How AAE is calculated for curve fitting and what does it's value indicate?

I have experimental results which are fitted to different equations, the fit is assessed by R^2 and AAE and I don't know how to interpret AAE values.
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1answer
393 views

Finding the appropriate polynomial fit in Python

Is there a function or library in Python to automatically compute the best polynomial fit for a set of data points? I am not really interested in the ML use case of generalizing to a set of new data, ...
2
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1answer
729 views

How to run a regression analysis in python on a nonlinear, strange dataset

I can't figure out what type of regression analysis or extrapolation technique to use in order to come up with an equation for the data I have plotted. For a school project, I've been testing diodes ...
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0answers
10 views

Definition of a 'design adaptive' fit?

When studying non-parametric regression, I've been told that local linear fitting is often better than local constant fitting at the job of estimating regression functions because local linear fitting ...
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1answer
60 views

What method can I use to produce a single curve from a number of curves?

I am looking for a good method to combine a set of curves into a single curve. Those curves have been produced by performing a measurement/testing n-number of times under similar conditions. What I ...
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0answers
35 views

model of two gaussion curves

How can I create in R a model that contains two Gaussian curves that describe that data I got. So I could get in the end the sigma and median of the Gaussian and calculate which datapoint belongs to ...
2
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1answer
31 views

Normalize Weights in fitting a curve

I am trying to fit a curve to set of data points. I have a set of weights that I want to assign each point while fitting. My question is that should i normalize the weights or use the weights as they ...
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2answers
44 views

Define prediction interval for a monthly sales pattern

The point of my analysis is to develop an alert system to detect when the sales of the current month are deviating significantly from the monthly forecast and guess whether the month is going to close ...
2
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1answer
85 views

Curve fitting in the presence of prior beliefs about the relationship between x and y

In the figure which follows each dot represents a game of a particular sport. The x-axis represents the home team's margin of victory, and so around the top-right we can see a game where a home team ...
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0answers
93 views

Fitting a logistic growth curve with an iterative formula in R

I'm trying to fit a logistic growth curve to specific countries GDP data using an equation, $P_{n+1} = rP_n(1-\frac {P_n}{k})$. (1) I've found constants $r$ and $k$ simply by finding a ...