# [R-SIG-Mac] polynomial issue

Ken Beath ken at kjbeath.com.au
Sat Nov 6 07:01:38 CET 2010

```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) + coef(p12)*(x^1) + coef(p12)*(x^2) + coef(p12)*(x^3) + coef(p12)*(x^4) + coef(p12)*(x^5) + coef(p12)*(x^6) + coef(p12)*(x^7) + coef(p12)*(x^8) + coef(p12)*(x^10) + coef(p12)*(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
>> _______________________________________________
>> R-SIG-Mac mailing list
>> R-SIG-Mac at stat.math.ethz.ch
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mac
>
> David Winsemius, MD
> West Hartford, CT
>
> _______________________________________________
> R-SIG-Mac mailing list
> R-SIG-Mac at stat.math.ethz.ch
> https://stat.ethz.ch/mailman/listinfo/r-sig-mac
>

```