Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [curve-fitting]

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

652 questions
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Fourier data with non-integer periods, correcting for phase bias

I have data that I believe is sinusoidal, but I don't have an integral number of periods. How do I find the "best fit" Sin/Cos function, compensating for this and for the ugly constant that appears? EXAMPLE: Here is some data that follows a…
user1566
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1 answer

Friendly alternative to sums of exponentials?

Physical and biological processes often exhibit (exponential) decay on multiple timescales. A standard approach to modelling such a decay is to fit a sum of of exponentials $$ y(t) = \sum_k a_k \mathrm{e}^{-t/\tau_k} $$ where $\tau_k > 0$ is the…
Estacionario
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Why/When might it be preferable to fit to the integral of the data, rather than to the data itself?

I am working on reducing the data from a particular type of particle detector. When struck by a particle, this detector produces a voltage pulse that has the form of a Gaussian convolved with an exponential decay. Among the earlier work done with…
Colin K
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Exponential decay function

I have a model where I assumed a variable X would have an exponential decay over time t. I modeled it in R as $$N = N_1e^{kt},$$ where $k < 0$ and $t$ is 1:95. However, looking are some real data that I have captured, it seems that the decay is…
JPT
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Meaning of correlation of fitted nonlinear curve parameters

Suppose that I have a curve $y(x|\theta)$, where $\theta$ are a set of parameters. My data set is tables $y_{ij}$ and $x_{ij}$. I fit the curve for each row $i$, and obtain the set of parameters $\hat\theta_i^k$ that best fit to this row, where $k$…
Aksakal
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Finding a function for data points with disturbances

I have a question regarding how to find an equation for data points that have disturbances. For example, I have the following data: P = 366 measured values T = 366 measured values t = [ 1 : 366 ], representing the days of the year (index) So at…
eng_sub
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What family of functions could that be?

I would like to find an analytical expression for a family of function that would look like the curves in the plot. Essentially ranging from the identity function up to sqrt kind of curve. What matters is that it must be concave and display some…
Junior Hechinger
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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 parabola. I want to quantify the quality if fit.…
nimbus3000
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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. What is the best model/method to use for this?
Jan Pickard
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Determining if two growth curves are significantly different

I am developing an artificial model to simulate the growth of two types of biological cells under different conditions. The data I obtained from my model takes the form of two data-sets representing the number of cells in the culture across time in…
MrD
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Fitting a quadratic through 5 points, goal is to find the maximum

I have some physical experiments done at various locations. The locations produces a set of observations y for one value of x, the independent variable. In the end across a set of locations I have values in the following form [y11, y21, y31, y41,…
gbh.
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Does a best fit make sense in this case?

I have collected data from 60 candidates, 30 female and 30 male, measuring their pain tolerance, or rather time able to withstand pain. I have plotted the times against the $n$th candidate: Would it make sense to compute curves of best fit? My…
Omer Cooper
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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? I am asking this because I can get the data…
Neeladri Reddy
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Which function matches this concave pattern in my scatter plot?

I'm trying to find a function that matches the following shape. My first attempt was with a cosine function $$ f(x) = a\cos(b x)$$ which yields the following result: What modification of the cosine function could help to make it better fit the…
jak
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Estimate rotation matrix from correlation of samples on a sphere

I have a process that produces samples on a sphere. I don't know the center or radius of the sphere, and the samples are highly non-uniform -- as a somewhat example, I have 90% of them in one quadrant of the sphere, and another octant might be…
Alex Meiburg
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