[R] Polynomial equation

[Moshe Olshansky]

Hi Chris,

Curve fitting has nothing to do with statistics (even though it is used in statistics).
To get an idea of this, try the following:

x <- ((-100):100)/100    
cofs<-rnorm(4)    #create coefficients
y <- cofs[1] + cofs[2]*x + cofs[3]*x^2 +cofs[4]*x^3
y1 <- y +rnorm(201,0,0.1)    #add noise
mm <- lm(y1~poly(x,3,raw=TRUE))    #fit a polynomial of degree 3
y2 <- predict(mm,as.data.frame(x))   #compute the polynomial for every point of x
plot(x,y,type="l");lines(x,y1,col="red");lines(x,y2,col="blue")
cofs
mm$coefficients

For the exponential fit, there exist two options:
you are trying to fit y = exp(a*x+b)
one possibility is to fit log(y) = a*x+b by mm <- lm(log(y)~x) 
and the other (more "correct") one is to use any of the least squares packages.

I believe that you better read a little bit about curve fitting before doing all this.

Regards,

Moshe.


--- On Fri, 8/1/10, chrisli1223 <chrisli at austwaterenv.com.au> wrote:

> From: chrisli1223 <chrisli at austwaterenv.com.au>
> Subject: Re: [R] Polynomial equation
> To: r-help at r-project.org
> Received: Friday, 8 January, 2010, 2:14 PM
> 
> Thank you very much for your help. Greatly appreciated!
> 
> However, due to my limited stats background, I am unable to
> find out the
> equation of the trendline from the summary table. Besides,
> how do I fit the
> trendline on the graph?
> 
> I intend to put the first column of data onto x axis and
> the second column
> onto y axis. Are they the x and y in your example?
> 
> Many thanks,
> Chris
> 
> 
> Moshe Olshansky-2 wrote:
> > 
> > Hi Chris,
> > 
> > You can use lm with poly (look ?lm, ?poly).
> > If x and y are your arrays of points and you wish to
> fit a polynom of
> > degree 4, say, enter:  model <-
> lm(y~poly(x,4,raw=TRUE) and then
> > summary(model)
> > The raw=TRUE causes poly to use 1,x,x^2,x^3,...
> instead of orthogonal
> > polynomials (which are "better" numerically but may be
> not what you need).
> > 
> > Regards,
> > Moshe.
> > 
> > --- On Fri, 8/1/10, chrisli1223 <chrisli at austwaterenv.com.au>
> wrote:
> > 
> >> From: chrisli1223 <chrisli at austwaterenv.com.au>
> >> Subject: [R]  Polynomial equation
> >> To: r-help at r-project.org
> >> Received: Friday, 8 January, 2010, 12:32 PM
> >> 
> >> Hi all,
> >> 
> >> I have got a dataset. In Excel, I can fit a
> polynomial
> >> trend line
> >> beautifully. However, the equation that Excel
> calculates
> >> appear to be
> >> incorrect. So I am thinking about using R.
> >> 
> >> My questions are:
> >> (1) How do I fit a polynomial trendline to a
> graph?
> >> (2) How do I calculate and display the equation
> for that
> >> trendline?
> >> 
> >> Many thanks for your help. Greatly appreciated.
> >> 
> >> Chris
> >> -- 
> >> View this message in context:
> >> http://n4.nabble.com/Polynomial-equation-tp1009398p1009398.html
> >> Sent from the R help mailing list archive at
> Nabble.com.
> >> 
> >> ______________________________________________
> >> R-help at r-project.org
> >> mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide
> >> http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained,
> >> reproducible code.
> >>
> > 
> > ______________________________________________
> > R-help at r-project.org
> mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained,
> reproducible code.
> > 
> > 
> 
> -- 
> View this message in context: http://n4.nabble.com/Polynomial-equation-tp1009398p1009438.html
> Sent from the R help mailing list archive at Nabble.com.
> 
> ______________________________________________
> R-help at r-project.org
> mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
>