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

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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 ...
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9 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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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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41 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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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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65 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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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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56 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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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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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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13 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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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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13 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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36 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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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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49 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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51 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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375 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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29 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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190 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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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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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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37 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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36 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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35 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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114 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 ...
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194 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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36 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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12 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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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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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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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 ...
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What function fits these criteria?

I want to use a function $f(x)$ to model my data $x$, where $x > 0$, and then fit the function's parameters to that data. My requirements are that $f(x)$ is continuous and smooth, $f(0) = 0$, $f(x) ...
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Fitting data to multimodal distributions with scipy, matplotlib

I have a dataset that I would like to fit to a known probability distribution. The intention is to use the fitted PDF in a data generator - such that I can sample data from the known (fitted) PDF. ...
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Fitting function to unreliable data - simultaneous optimization of parameters and observations

I try to fit noisy (biophysical) data. The data are expected to fit a relatively simple, two parameter function. My measurement is flawed in a way that introduces systematic errors to my data. I ...
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774 views

Simple Log regression model in R

I am trying to fit a regression model, as the plot says the relation is log. I tried to use lm(logData$x ~ logData$b3, data = logData) but it did not work ...
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How do I estimate a smooth cdf from a set of observations?

I have a set of observation, let's call it $X$ and would like to fit a cdf to it. $X$ has a distribution which is roughly approximable with the normal distribution. This CDF should correspond to a ...
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Creating data to fit some curves

I am not a statistician and I am not expert in R, but I know to use some codes. I need to plot some curves which I got their R codes to plot, but I need to create the data (samples) for some simple ...
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Why are the basis functions for natural cubic splines expressed as they are? (ESL)

I'm doing some self-study with ESL (http://www-stat.stanford.edu/~tibs/ElemStatLearn/download.html) and I've come to 5.2.1, the section on natural cubic smoothing splines and I'm having conceptual ...
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Select a fittting model for histograms varying the number of Gaussians

I have many data in the form of one dimensional histogram, to give an example consider the data at http://pastebin.com/embed_js.php?i=1mNRuEHZ I expect that these data are obtained from a pdf ...
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27 views

Why fitting does not find the true best point

I fitting an expression of the form: $s(t)=\frac{1}{1+\exp[a+\sum_k b_k x_k(t)]}$ Where $a$ and $b_k$ are fitting parameters and $x_k(t)$ an input time series. I have $k=1,...,N$ different types of ...
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522 views

Fitting known equation to data

I have measured growth rates over a range of temperatures (temperature response curve) and would like to fit an already established equation/model to it. I'm very new to R and have trouble coding it ...
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124 views

Fluctuations in hazard function at high (x) values

Using a best-fit algorithm, i've obtained gamma-distribution parameter MLEs for my data (scale and shape). When evaluating the hazard function, calculated as the PDF divided by the reciprocal CDF, ...
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Weibull fitting

I'm trying to fit a Weibull curve to my xy data. I know that the 3 Weibull model has 3 parameters, the scale, the shape and the location and I would like to estimate them from my data. I used curve ...
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82 views

R - fitting a gamma distribution given the CDF?

I'm trying to develop a prediction model of the success or failure of a test run based on its current running time (in my data, from observation, the longer a test runs the more likely it is to fail). ...
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30 views

plot integer data on a log-log scale

I'm new to statistics, and this may be a very trivial problem. I have an array of sorted data: ...
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Fitting to a sum (mixture?) of components

I have a curve-fitting problem in which I'm fitting my data to a sum of components with identical functional forms but different parameters. That is $d_i = f(x_i | \theta_j) + f(x_i | \phi_j) + ...