# [R] Regression on non linear model

Douglas Bates bates at stat.wisc.edu
Thu Oct 14 04:13:55 CEST 1999

```Peppy <s.adi.purnomo at EnergyLink.co.nz> writes:

> Dear Help desk,

An interesting concept - the R "Help desk" is in fact a mailing list.

> I have a model that I believe to be non linear.  The relationship is
> something like:
>
> Response = Var1 + Var1^2 + Var1^3

In terms of the way the parameters enter the model, this is still a
linear model, even though it is nonlinear in terms of the variable.

> Can I examine this relationship using glm or lm?  However, glm or lm gives
> out pnly 1 coeficient for the model which is on Var1,  unless I created some
> dummy var like (Var2 = Var1^2 and Var3 = Var1^3).

You are correct.  This is a deficiency in the model formula language
used in R.  The meaning of the ^2 operator in formulas is appropriate
for factors but not the expected meaning for numeric variables.

> Is there any other function handling this relationship?

The preferred way to do this is to use the I() function to protect
the ^2 and ^3 from being evaluated as part of the linear model
formula.  That is, write the call to lm with

formula = Response ~ Var1 + I(Var1^2) + I(Var1^3)

> My R is 0.64.2

The most recently released version is 0.65.1.  As R is freely
available it is probably a good idea to upgrade.
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```