# Questions tagged [nonlinear-regression]

Use this tag only for regression models in which the response is a nonlinear function of the parameters. Do not use this tag for nonlinear data transformation.

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21k views

### How to tell the difference between linear and non-linear regression models?

I was reading the following link on non linear regression SAS Non Linear. My understanding from reading the first section "Nonlinear Regression vs. Linear Regression" was that the equation below is ...
23k views

### Why is polynomial regression considered a special case of multiple linear regression?

If polynomial regression models nonlinear relationships, how can it be considered a special case of multiple linear regression? Wikipedia notes that "Although polynomial regression fits a nonlinear ...
3k views

### Do statisticians assume one can't over-water a plant, or am I just using the wrong search terms for curvilinear regression?

Almost everything I read about linear regression and GLM boils down to this: $y = f(x,\beta)$ where $f(x,\beta)$ is a non-increasing or non-decreasing function of $x$ and $\beta$ is the parameter you ...
8k views

### What is the most appropriate way to transform proportions when they are an independent variable?

I thought I understood this issue, but now I'm not as sure and I'd like to check with others before I proceed. I have two variables, X and ...
4k views

### Linear regression best polynomial (or better approach to use)?

Any ideas on other polynomials I could successfully use for applying regression? My goal is a solution that has fit error strictly based on the noise. Is this possible since it is a bell-like curve? ...
43k views

### How do I test a nonlinear association?

For plot 1, I can test the association between x and y by doing a simple correlation. For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test the ...
10k views

### How to compute prediction bands for non-linear regression?

The help page for Prism gives the following explanation for how it computes the prediction bands for non-linear regression. Please excuse the long quote, but I am not following the second paragraph (...
1k views

### Exponent for non-linear regression (in R)?

I have a non-linear reglationship and I want to find the best way to determine the value for the exponent $\gamma$ in the following regression: $y = \beta x ^ \gamma$ I would preferably like to do ...
3k views

### Why is my high degree polynomial regression model suddenly unfit for the data?

I'm building a ridge regression model in scikit-learn and trying to find the optimal degree polynomial to use. The data I'm working with is a fairly predictable time series of hourly traffic volumes, ...
7k views

### How to minimize residual sum of squares of an exponential fit?

I have the following data and would like to fit a negative exponential growth model to it: ...
3k views

### nls curve fitting of nested/shared parameters

I'm trying to fit raw data to curves, which works well on an individual basis. However, I'd like to "share" parameters (sometimes referred as nested parameters) across more than one data series. Is ...
16k views

### Distinction between linear and nonlinear model

I have read some explanations about the properties of linear vs nonlinear models, but still I am sometimes not sure if a model on hand is a linear or a nonlinear one. For example, is the following ...
1k views

### Linear vs. nonlinear regression

I have a set of values $x$ and $y$ which are theoretically related exponentially: $y = ax^b$ One way to obtain the coefficients is by applying natural logarithms in both sides and fitting a linear ...
5k views

### Help me fit this non-linear multiple regression that has defied all previous efforts

EDIT: Since making this post, I have followed up with an additional post here. Summary of the text below: I am working on a model and have tried linear regression, Box Cox transformations and GAM but ...
4k views

### Is least squares the standard method to fit a 3 parameters Gaussian function to some x and y data?

A participant in one experiment needs to decide whether a flash and a sound are simultaneous or not for many possible asynchronies between the flash and the sound (x in seconds). For each asynchrony, ...
14k views

### What does “curvilinear” mean?

As far as I can tell, curvilinear is defined vaguely but means the same as nonlinear. Is that correct? Or does curvilinear have a distinct definition?
2k views

### Strange outcome when performing nonlinear least squares fit to a power law

I have a data set (given below in my MATLAB code) y vs. x and my eventual goal is to fit it to a power law $y=ax^b$ to see what exponent $b$ I get. I did some non-linear least squares fitting and ...
511 views

### Analyze scatter plot

I want to study the relationship between two variables. I've got the following scatter plot. But now I'm hesitating on what to do with this: Should I check the assumptions of OLS and then use the lm ...
172k views

### What does the hidden layer in a neural network compute?

I'm sure many people will respond with links to 'let me google that for you', so I want to say that I've tried to figure this out so please forgive my lack of understanding here, but I cannot figure ...
6k views

### Regression for a model of form $y=ax^k$?

I have a dataset which is statistics from a web discussion forum. I'm looking at the distribution of the number of replies a topic is expected to have. In particular, I've created a dataset which has ...
43k views

### Singular gradient error in nls with correct starting values

I'm trying to fit a line+exponential curve to some data. As a start, I tried to do this on some artificial data. The function is: $$y=a+b\cdot r^{(x-m)}+c\cdot x$$ It is effectively an exponential ...
19k views

### How to choose initial values for nonlinear least squares fit

The question above says it all. Basically my question is for a generic fitting function (could be arbitrarily complicated) which will be nonlinear in the parameters I am trying to estimate, how does ...
21k views

### Linear regression what does the F statistic, R squared and residual standard error tell us?

I'm really confused about the difference in meaning regarding the context of linear regression of the following terms: F statistic R squared Residual standard error I found this webstie which gave ...
17k views

### What's the most pain-free way to fit logistic growth curves in R?

This isn't as easy to Google as some other things as, to be clear, I'm not talking about logistic regression in the sense of using regression to predict categorical variables. I'm talking about ...
10k views

### Shape of confidence and prediction intervals for nonlinear regression

Are the confidence and prediction bands around a non-linear regression supposed to be symmetrical around the regression line? Meaning they do not take on the hour-glass shape as in the case of the ...
126 views

### Pitfalls in Fitting Nonlinear Models by Transforming to Linearity

Some nonlinear models can be transform to linear models. My understanding is that there might be one-to-one relationship between the estimates of nonlinear model and its linear model form but their ...
4k views

### What are the formulas for exponential, logarithmic, and polynomial trendlines?

In creating linear trendline, I used the following formulas: $$y=mx+b$$ $$m = \frac{n\sum(xy)-\sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y- m \sum x}{n}$$ and this for the R-squared: ...
962 views

### Behavior of $R^2$ in non-linear models

I am a bit stumped on the behavior of $R^2$ in non-linear models. Below is some data and two hyperbolic fits. One in which two parameters are estimated (Model $m_1$), and another in which one ...
224 views

### Modern approaches to nonlinear regression which are available in R

I would like to fit a complex nonlinear regression model: basically, I have a complex computer code which has an input vector $\mathbf{x}$, a vector of calibration parameters $\boldsymbol{\theta}$ and ...
14k views

### Incidental parameter problem

I always struggle to get the true essence of the incidental parameter problem. I read in several occasions that the fixed effects estimators of nonlinear panel data models can be severely biased ...
279 views

### Can we use bootstrap samples that are smaller than original sample?

I want to use bootstrapping to estimate confidence intervals for estimated parameters from a panel dataset with N=250 firms and T=50 month. The estimation of parameters is computationally expensive (...
787 views

### Fit a smooth approximation line

I have a simulated data set and I want to fit a "smooth approximation line" like the image I have provided. 1- Is it possible to do this in Excel or Matlab? May I have a pointer on how to do it? 2- ...
4k views

### Estimation of exponential model

An exponential model is a model described by following equation: $$\hat{y_{i}}=\beta_{0}\cdot e^{\beta_{1}x_{1i}+\ldots+\beta_{k}x_{ki}}$$ The most common approach used to estimate such model is ...
762 views

### What is the difference between GLM and splines?

Suppose we want to predict $Y$ given the following $X$ observations: ...
320 views

### Identifiability in a nonlinear regression problem

Suppose I'm working with the following model $y_i = \alpha(1-\exp(-\beta t_i))+\gamma(1-\exp(-\delta t_i)) + \varepsilon_i$. The $\varepsilon_i$ are i.i.d. gaussian with zero mean and I'm trying to ...
6k views

### How to test a curvilinear relationship in a logistic regression

I was looking for some information about curvilinear relationships (quadratic function, to be precise) in logistic regression online, and couldn't really find much about it. I am interested if that ...
1k views

### Non-linear least squares standard error calculation in R

I am using implementations of the Levenberg-Marquardt algorithm for non-linear least squares regression based on MINPACK-1 utilizing either the R function nlsLM() from minpack.lm or an implementation ...
11k views

### How to perform an exponential regression with multiple variables in R

I'd like to perform an exponential regression with multiple independent variables (similar to the LOGEST function in Excel) I'm trying to model the function $Y = b {m_1}^{x_1}{m_2}^{x_2}$ where $b$ ...
298 views

### Regression when response variable is a function

I have a set of data $(X_i,Y_i)$, $i=1,\ldots,n$ where $X$ and $Y$ are supposed to satisfy the following equation $$y = \beta_0(1+x^2)^{\beta_1},\quad x>0, \quad\quad (1)$$ I am interested in ...
775 views

### Question about prediction bands for non-linear regression computation?

I am interested in computing prediction bands for a non-linear regression (log-logistic function with 3 parameters). I have read the Prism help page: The calculation of the confidence and ...
260 views

### Forecasting recurring orders for an online subscription business using Facebook Prophet and R

I am analyzing data from a subscription model, in which a customer must pay a recurring price at a regular interval (30 days) for access to the product. EDIT -> Direct link to daily data: https://...
163 views

### Kernel ridge regression with matrix-vector data set $S := \{ X_i, y_i \}_{i=1}^{N}$?

Please notice that this question was asked in MO, but it seems that it doesn't interest MO community. So, I have got a comment to post in this community in the hope that I may get some attention to ...
142k views

### How to add non-linear trend line to a scatter plot in R? [closed]

I have a scatter plot. How can I add non-linear trend line?
11k views

### Non-linear mixed effects regression in R

Surprisingly, I was unable to find an answer to the following question using Google: I have some biological data from several individuals that show a roughly sigmoid growth behaviour in time. Thus, I ...
32k views

### When fitting a curve, how do I calculate the 95% confidence interval for my fitted parameters?

I am fitting curves to my data to extract one parameter. However, I am unsure what the certainty of that parameter is and how I would calculate / express its $95$% confidence interval. Say for a ...
407 views

### OLS as approximation for non-linear function

Assume a non-linear regression model \begin{align} \mathbb E[y \lvert x] &= m(x,\theta) \\ y &= m(x,\theta) + \varepsilon, \end{align} with $\varepsilon := y - m(x,\theta)$...
17k views

### what makes neural networks a nonlinear classification model?

I'm trying to understand the mathematical meaning of non-linear classification models: I've just read an article talking about neural nets being a non-linear classification model. But I just realize ...
2k views

### fitting an exponential function using least squares vs. generalized linear model vs. nonlinear least squares

I have a data set that represents exponential decay. I would like to fit an exponential function $y = Be^{ax}$ to this data. I've tried log transforming the response variable and then using least ...