[R-SIG-Mac] polynomial issue

[Ken Beath]

On 06/11/2010, at 12:30 PM, David Winsemius wrote:

> 
> On Nov 5, 2010, at 7:05 PM, Ivan Cabrera wrote:
> 
>> Hi all, I'm new to any programming and I've been doing some stuff in R the last couple of month, I hope you can help me here…
>> 
>> I'm using lm() to do a 12 degree polynomial fit to a series of data x,y. Then I built a polynomial using the coefficients given by coef() function (replacing any NA by a 0), and evaluate it in x.
> 
> This does really look more like an Rhelp question.
> 
>> 
>> > x<-data[,1]; y <- data[,2]
>> > pol <- paste(paste("I(x",1:12,sep="^"),")",sep="")
>> > form <- as.formula(paste("y~", paste(pol,collapse="+")))
>> > p12 <- lm(form)
>> > coef(p12)
>> (Intercept)        I(x^1)        I(x^2)        I(x^3)        I(x^4)        I(x^5)        I(x^6)        I(x^7)        I(x^8)        I(x^9)       I(x^10)
>> 1.549683e+05 -2.801410e+02  2.238321e-01 -1.037342e-04  3.071376e-08 -6.013217e-12  7.735856e-16 -6.168457e-20  2.493099e-24            NA -3.184072e-33
>>     I(x^11)       I(x^12)
>>          NA  3.973316e-42
>> > pl12 <- coef(p12)[1] + coef(p12)[2]*(x^1) + coef(p12)[3]*(x^2) + coef(p12)[4]*(x^3) + coef(p12)[5]*(x^4) + coef(p12)[6]*(x^5) + coef(p12)[7]*(x^6) + coef(p12)[8]*(x^7) + coef(p12)[9]*(x^8) + coef(p12)[11]*(x^10) + coef(p12)[13]*(x^12)
>> 
>> My problem comes when I replace the coef(p12)[ ] with their actual values. I get completely different values of the polynomial…
> 
> I am wondering what would happen if you tried:
> 
> fit12 <- lm(y ~ poly(x), degree=12)
> 
> p12 <- predict(fit12)
> 
> plot(p12)
> 

Yes,  a numerical problem. The two NA in the coefs make this a certainty. Using (and understanding poly) will solve the problem. However in most cases using splines will produce something closer to the result you want. While a polynomial will fit the points well, it is likely to do ridiculous things between the points.

Further questions should be directed to Rhelp or a general stats list.

Ken

> (Untested in absence of reproducible data.)
> 
> -- 
> David.
> 
> 
>> 
>> > pl12.1 <- (1.549683e+05) + (-2.801410e+02)*(x^1) + (2.238321e-01)*(x^2) + (-1.037342e-04)*(x^3) + (3.071376e-08)*(x^4) + (-6.013217e-12)*(x^5) + (7.735856e-16)*(x^6) + (-6.168457e-20)*(x^7) + (2.493099e-24)*(x^8) + (-3.184072e-33)*(x^10) + (3.973316e-42)*(x^12)
>> > rle(pl12==pl12.1)
>> Run Length Encoding
>> lengths: int 3412
>> values : logi FALSE
>> 
>> and not even the shape of the functions are alike when i plot them.
>> 
>> can anyone give me a clue of what's happening and how to fix it?
>> 
>> Thanks,
>> Ivan
>> _______________________________________________
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>> R-SIG-Mac at stat.math.ethz.ch
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> 
> David Winsemius, MD
> West Hartford, CT
> 
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