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If you were to specify sufficient information about the exact circumstances (e.g. it's a regression, with this much nonlinearity, that amount of variation in this independent variable, this kind and amount …

This allows you to fit particular forms of nonlinear relationship between $y$ (or rather its conditional mean) and the $x$-variables; while you can do this in nls as well, there's no need for starting … So - in relation to the title question - you can fit a substantially wider variety of Gaussian models with a GLM than with regression. …

regression model model: cost.per.car ~ a * exp(b * reductions) + c data: q24 a b c 0.003289 0.126805 48.487386 residual sum-of-squares: 2243 Number of iterations to … In some circumstances, a sequence of nonlinear fits is made where you can expect the solutions to change slowly. …

While the linear model approach discussed here is simple to use, one advantage of @COOLSerdash's nonlinear regression approach is that it can deal with a much wider range of situations - you don't have … to change much before you're in a situation where linear regression is no longer suitable but nonlinear least-squares may still be used (having an unknown period would be one such case). …

How to specify the knots in R The ns function generates a natural regression spline basis given an input vector. …

John Fox's book An R companion to applied regression is an excellent ressource on applied regression modelling with R. … Modelling nonlinear relationships Two quite flexible methods to fit nonlinear relationships are fractional polynomials and splines. …

I want to perform ... linear regression in R. ... I would like the slope to be inside an interval, let's say, between 1.4 and 1.6. How can this be done? (i) Simple way: fit the regression. … So lets use the constrained regression in nls: nls(y~a+b*x,algorithm="port", start=c(a=0,b=1.5),lower=c(a=-Inf,b=1.4),upper=c(a=Inf,b=1.6)) Nonlinear regression model model: y ~ a + b * x data …

My general approach to this is graphical exploration of the raw data and regression diagnostics ... …

The simplest R function to do this is nls. (The R code I used is at the end of the answer.) … R code In terms of R code, it was simplest to define a general function for your temperature-response curve: trcFunc <- function(x,z,a,b){((a-x)/(a-z))*((x/z)^(z/b))} then give specific values for …

A good compromise is to allow all main effects to be nonlinear using regression splines such as restricted cubic splines (natural splines). … For example, we can assess the combined contributions of nonlinear or interaction terms or both. An example follows, using the R rms and quantreg packages. …

It has a low $R^2$, indicating a lot of scatter and strong "regression to the mean": the regression line has a smaller slope than the major axis of this elliptical point cloud. … The same fit is plotted: now it looks curved due to the nonlinear way in which log odds are converted to probabilities. …

There are several distinctions between linear and nonlinear regression models, but the primary mathematical one is that linear models are linear in the parameters, whereas nonlinear models are nonlinear … Pinheiro and Bates (2000, pp. 284-285), authors of the nlme R package, elegantly described the more substantive considerations in model selection: When choosing a regression model to describe how a …

regression method. … I recall seeing a couple papers describe this kind of approach as a way to perform out-of-sample generalization for nonlinear dimensionality reduction algorithms in general. …

I am answering by pasting Douglas Bates's reply in the R-Sig-ME mailing list, on 17 Dec 2014 on the question of how to calculate an $R^2$ statistic for generalized linear mixed models, which I believe … The proposal was to examine I think 9 different formulas that could be considered ways of computing an R2 for a nonlinear regression model to decide which one was "best". …

In my opinion, it's a good strategy to transform your data before performing linear regression model as your data show good log relation: > #generating the data > n=500 > x <- 1:n > set.seed(10) > y < … : 0.5236, Adjusted R-squared: 0.5226 F-statistic: 547.3 on 1 and 498 DF, p-value: < 2.2e-16 > > coef(fit) (Intercept) log(x) -6.469869 1.087886 > > #plot > x=seq(from=1,to=n,length.out …