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.

Nonlinear regression concerns models that are inherently nonlinear: that is, they cannot be expressed as a linear combination of parameters $\beta$. It is practically the same thing to say that a nonlinear model cannot be put into the form $Y = X\beta + \epsilon$ after a preliminary mathematical re-expression of $X$, $Y$, or both. For example, $Y = \log(X)\beta + \epsilon$ and $Y = \exp(X\beta + \epsilon)$ are both linear whereas $Y = exp(X\beta) + \epsilon$ and $Y = \log(X + \beta) + \epsilon$ are nonlinear.

(As usual, $Y$ is a dependent variable (or vector thereof), $X$ is a vector of independent variables, $\beta$ is a set of parameters to be estimated, and $\epsilon$ is random "error" with zero mean.)

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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 out how the practical implementation of a neural…
FAtBalloon
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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 association and label its nature?
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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 model to the data, as a statistical estimation…
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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 actually a linear regression, is that correct? If…
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Why is nls() giving me "singular gradient matrix at initial parameter estimates" errors?

I have some basic data on emission reductions and cost per car: q24 <- read.table(text = "reductions cost.per.car 50 45 55 55 60 62 65 70 70 80 75 90 80 100 85 200 90 375 95 600 ",header = TRUE,…
Amanda
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How to add non-linear trend line to a scatter plot in R?

I have a scatter plot. How can I add non-linear trend line?
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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 curve with a linear section, as well as an…
steiny
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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 fitting a logistic growth curve to given data points.…
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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 because of the "well-known" incidental parameter…
emeryville
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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 a list of topic reply counts, and then the count…
thenickdude
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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 me great insight in the different terms involved…
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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 (that explains how $G|x$ is defined and $dY/dP$ is…
Joe Listerr
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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 estimate and test hypotheses about. There are…
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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 model: > fit <- lm(log(y)~log(x)) > a <-…
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Use of standard error of bootstrap distribution

(ignore the R code if needed, as my main question is language-independent) If I want to look at the variability of a simple statistic (ex: mean), I know I can do it via theory like: x = rnorm(50) # Estimate standard error from…
John Colby
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