Questions tagged [curve-fitting]

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

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What's the use of curve fitting for a function $y = f(x)$, if I can reduce it to a linear regression?

Suppose I have data points $(x_i,y_i)$, say $N$ points. I know they are supposed to fit the curve $y = f(x)$. Are there techniques more advanced than linear regression, for such cases to fit the curve?...
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Classifying multivariate data as gaussian, non-gaussian, or a mixture of gaussians?

It's for the following use case: I have a set of "detects" of a group of individual targets (mostly stationary) that I wish to cluster or segment such that each cluster (group of detects) ...
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Fitting a well-specified 1D function of time to 3D spatial and spatially correlated data

I have acquired experimental data that can be considered to be a scalar field in physical three-dimensional space, $(x,y,z)$ that I have observed over time, measured on an equally spaced regular grid. ...
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Forecasting two dependent count variables using single independent variable (Time)

I'm stuck with a modeling problem without any results in my org. The model first should be developed based on time (in M or W) in x axis and booking counts across y axis. Next it has to be identified ...
2 votes
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Logistic regression - Confidence interval for x axis

My question is very similar to the post Confidence interval for x-values given a probability in a logistic regression where ultimately no answer was given. I have also posted a similar version on the ...
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2 votes
1 answer
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What is the best method for fitting a curve that has the dependent variable on both sides of the equation?

I am trying to fit a curve to a set of measured data. Similar studies have been done, and the resulting curve fit is usually of the following form. $$\frac{1}{\sqrt{Y}}=a \log{\left(X \sqrt{Y}\right)}-...
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Confidence bounds for coefficients of a fit of data set obtained with another fit

I fitted an equation to a set of data points. Then I substracted the fit previously obtained to another set of data points. After that, I fitted another equation to this new data (result of the ...
2 votes
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How do I calculate the 95% confidence interval of a curve that depends on many parameters?

Assuming I have a curve fit that depends on 4 parameters. How would I compute the 95% confidence interval if I had many variations of this curve fit (many combinations of samples of these 4 parameters)...
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Logistic 3 Parameter (3pl) prediction model calculation

I´m currently working on a prediction model using Logistic 3P fit with JMP. I´m obtaining very good curves using the calculated fit model. The model is the following: y= c/{1+exp[a*(x-b)]} Where a is ...
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1 answer
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Predictions based on data with correlations within and between multiple sets of time series

I'm looking for a model to learn relationships within and between a set of partially observed time series in order to generate predictions for any timepoint in any of the set of time series. More ...
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How to calculate uncertanty of extremal point of fitted quadratic polynom?

I am doing some fitting in python, that is: ...
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Pick minimum value based on MSE and point

I am attempting to automate some processes at work. Im familiar with statisical methods such as GLM, ANOVAs, Basic OLS, etc. But I am unsure of methods which I can use for this. problem statement: ...
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Peak fitting using unknown formula

I was interested in determining what "full employment" meant in the US by looking at the various peaks in unemployment over time and trying to fit a model through it. My assumption based on ...
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1 answer
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Growth curve analysis in R - time variable as a polynomial

I have narrowed down some specific questions and was advised that it's more appropriate to post them here than on stackoverflow I'm building a growth curve model using lmer in R and I'm unsure about ...
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Growth curve modeling using lmer - how is it different from mixed effects regression?

EDIT: I'm realising time cannot be a random effect, is that right? Where does it fit with other fixed effects? Can time be a polynomial? I am trying to set up a growth curve analysis using lmer, I ...
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Using curve_fit for Non-Linear, Multi-Variate Models [Python] [closed]

Warning: ML Noob. I have a 3D dataset (data at the bottom) with 2 feature variables and 1 target variable. Polynomial Regression produced unsatisfactory results and it seems that the relationship of ...
2 votes
1 answer
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Unsupervised classification of objects based on relationships

I have size measurements of 1000 objects, measured over time. I would like to classify the objects based on the response of their size to time using unsupervised classification. For example, the size ...
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2 answers
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How does the TI-84 calculate the best fit for a logistic model?

Back in High School I remember the TI-84 calculator allowing the user to enter a few data points and then select from a list of options to find an equation that best fit the data points. One of these ...
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Combining data from multiple studies - best approach?

I'm looking at an old paper on the incidence of HPV infection by age cohorts. The authors present a plot of estimates from many different studies around Europe which looks like this - note the authors ...
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Recovering samples from a density estimation with an additional prior on the samples. Used for Gibbs sampling

Abstract Idea: Given a noisy measured density ($d_j$ at position $p_j$) and a density model, sample from the model parameters under the following stochastic model: Stochastic Model: Prior for model ...
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1 vote
1 answer
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Describing / fitting a highly skewed distribution

I've got a data set of 84,529 entries, each entry referring to the number of times a particular entry is cited in a database. This set is extremely skewed, ranging from entries with 0 citations to one ...
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How to fit joint models for longitudinal and binary (outcome) data?

Joint Models are mainly viewed in the literature within the context of longitudinal and time-to-event data. For this reason R packages as JMBayes were built to fit these kind of models. Nonetheless I ...
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How to predict single y target based on several X values? [duplicate]

I try to predict the result of an personality type test based on how people answered. My sample consists of the answers which range from 1 (strongly disagree) to 7 (strongly agree). Six answers lead ...
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Expand a Gaussian numerically with a basis of functions

I am asking a question that is math, but I am not sure if machine learning can help too, so posting here! I have a univariate Gaussian function $\phi_{\mu, \sigma}(x)$, with mean $\mu$ and variance $\...
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1 answer
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How to fit a gradual upward curve

I'm trying to fit a curve to my data (shown below), but I'm not sure of the best way to do it. I tried an exponential function following this tutorial, but it didn't fit the data at all (just a ...
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Advice on fitting curve to three-pooled plant decomposition model in r

I have just finished running a plant decomposition experiment measuring the decomposition of pine needles across climate and lithological types. We have mass loss, plant chemistry data (c, n, labile ...
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How to incorporate standard error into non-linear model?

Suppose you have some function $f(x)$ which represents the mean value of an experiment related to $x$. Then $\epsilon = \sigma(x)/\sqrt{n}$ is the error associated with each point $x$. Assuming that ...
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comparing data regularity

I have data about ratings from 5 sessions, it appears that initially ratings are random, and with experience, they become more 'defined', settling into a pattern (see graph below). How can I test this ...
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Fitting a cubic-like curve to data in R

I tried using nls() in R to fit the following expression to a set of data: where g=9.8, alpha & B_0 are unknown, a = 0.01, z_0 = 0.3 such that: theory <- as.formula(V~-(9.8)ab*(pi)(0.02^2)(T)(...
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Fitting data with a N-dimmenstional matrix

For my thesis I should fit my data points to a concept from statistical physics - Zimm-Bragg model. Let us consider a chain build of blocks in a state H. When i heat up the sample the blocks can ...
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Exponential fitting in R with fixed minimal value

I need approximate datapoints by exponential function with some type of lower limit (variable "y" is price in time and I need fixed minimal value, so asymptote of exponential function cant ...
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How to fit a distribution if the samples have not been draw randomly

I read the posts here and here. The real-life problem is: In a rare event simulation catastrophic events occur extremely seldom. The performance of my underlying system has an unknown distribution and ...
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1 answer
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Optimization (minimization) algorithm - hitting on boundaries

I'm struggling with a challenging optimization problem with real-world experimental data. Simply put, it's about fitting a exponential decay model to a curve (decay). Essentially, I am trying to ...
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2 answers
118 views

GAM with Beta-Binomial family on very large data

I am trying to fit a GAM on (success) counts assuming they follow a beta-binomial distribution. Each data point has three values: 1- Number of trials (N) 2- Number of successes (n) 3- A covariate (p) ...
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Error "propagation" under base change

Imagine you have fitted a curve to data in $x$-$y$-space and obtained errors $\sigma_x$ and $\sigma_y$ for each data point. But now you rotate the coordinate system by $45^\circ$ for example. Can you ...
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Should histograms be normalized first before fitting them?

Assume I have some data that follow a power law and I would like to estimate the exponent $a$. An obvious way to do so is to bin the data and then fit the power law to the histogram. However I found ...
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Roc curve straight line interpretation [duplicate]

How can I fix the straight line? is that mean that 70% of my cases that tag as positive and actually negative have the same value?
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Find a smooth function that maximizes a composite likelihood function

I need to find a smooth function $f$ that maximizes an objective function $g$ over its predictions on a predefined set of values $p$: \begin{equation} f^*=\arg\max_{f} g(f(.),p,X) \end{equation} In ...
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How to clean dataset in order to fit to a curve? [duplicate]

I'm trying to fit a dataset to a curve for while, but I'm not managing. The goal is to obtain a curve with equation that fits the data so I can get the parameter x to any value of y. The blue dataset ...
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Can "Curve Fitting" be seen as an Alternative to Numerical Differentiation?

For a long time, the following point always confused me: If the "Fundamental Theorem of Calculus" tells us that all real and continuous functions are differentiable (i.e. have derivatives) - ...
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Fitting two lines to convoluted data [duplicate]

Assume you are provided with data derived from two linear equations + noise, such as that below. How would you go about deconvoluting the lines, and obtaining their slopes/biases? Colab link for ...
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How can I validate my curve fitting meta-regression?

I'm doing a meta-regression analysis on Normal Pressure Hydrocephalus Gait Analysis. Studying the variation of gait velocity after a procedure (Tap-test). Keeping into account single study (#14) ...
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Which test to use to test for heteroscedasticity in a non linear model/fit?

I would like to test for heteroscedasticity in a non linear fit. I have a explanatory vector x and an explained variable y and ...
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1 vote
1 answer
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In univariate linear regression if you are already using Ordinary Least Square, is cost function still neccesary?

I have a question regarding cost function and Ordinary Least Square (OLS) in univariate linear regression. From my understanding, in linear regression, OLS is used to find the the slope and y-...
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Departure from uniformity histogram

Let us consider the histogram of a random variable. It is uniform up to a certain value $\bar{x}$, while beyond it a growth is present,as shown in the figure. I would like to obtain an estimate of the ...
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Fitting Several Linear Regressions at Once

Suppose I have n stocks. X_1 ... X_n. In turn I want to predict the returns Y_1 ... Y_100 over some horizon t. Ultimately ...
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Fitting a distribution to my data, and estimating future transactions

Assuming that I have a list of transactions generated by an unknown process. After fitting a distribution to my data I wish to report the projected sum of n transactions - assuming that it's generated ...
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Fit a Gaussian function (not a Gaussian distribution) to data

I am trying to train a Gaussian function. NOTE: Since we're on a Q&A site with one of its focuses being Statistics, it is worth emphasizing that not all Gaussian functions are normal ...
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Quadratic curve fit while constraining a term

I get sets of points that are generally linear with slight curvature to them. We've been fitting quadratic curves to them which works fine if we have decent points across the range but if there are ...
-1 votes
1 answer
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Interpolation based on a known curve

I have 6 datasets, 1 of which has 20 points, the other five have only 2 (beginning and end points). I want to interpolate 18 intervening points into the 2 point datasets such that the resulting curves ...

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