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Polynomial equation

4 messages · Moshe Olshansky, chrisli1223

chrisli1223
# 
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
Moshe Olshansky
# 
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:

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      chrisli1223
    

    

      
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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:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Moshe Olshansky
    

    

      
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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: