# SSpoly2: Simple polynomial regression functions In OnofriAndreaPG/aomisc: Statistical methods for the agricultural sciences

 poly2 R Documentation

## Simple polynomial regression functions

### Description

These functions provide the simple polynomial (second order) regression model (poly2), the polynomial regression model with self-starter for the `nls` function (NLS.poly2) and the polynomial regression function with self-starter for the `drm` function in the drc package (DRC.poly2). Fitting linear functions with nonlinear least square regression is sub-optimal, but it might be useful for comparing alternative models.

### Usage

``````  poly2.fun(predictor, a, b, c)
NLS.poly2(predictor, a, b, c)
DRC.linear(fixed = c(NA, NA, NA), names = c("a", "b", "c"), ...)
``````

### Arguments

 `a` numeric. The response when the predictor is equal to 0. `b` numeric. The slope at X = 0 `c` numeric. Regression parameter `fixed` numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. `names` a vector of character strings giving the names of the parameters. The default is reasonable.

### Details

The simple polynomial (second order) regression model is given by the following equation:

` f(x) = a + b x + c x^2`

### Value

poly2.fun and NLS.poly2 return a numeric value, while DRC.poly2 returns a list containing the nonlinear function, the self starter function and the parameter names.

Andrea Onofri

### References

Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.

Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/

### Examples

``````# Polynomial regression
X <- seq(5, 50, 5)
Y <- c(12.6, 74.1, 157.6, 225.5, 303.4, 462.8,
669.9, 805.3, 964.2, 1169)

model <- nls(Y ~ NLS.poly2(X, a, b, c))
summary(model)
model <- drm(Y ~ X, fct = DRC.poly2())
summary(model)
``````

OnofriAndreaPG/aomisc documentation built on July 4, 2023, 6:53 p.m.