R help - Jun 2010 - fit data with y = x^-1

Dear list,

I am getting weired with fitting data with a 1/x-polynomial. Suggest I have
the following data:

x <- c(1,2,3,4,5,6,7)
y <- c(100,20,4,2,1,.3,.1)

I may fit this with a linear model

fit1 = lm(y ~ I(x))

Getting plot out of this model I applied
library(polynom)
pol1 = polynomial(fit1$coefficients)
f1 = as.function(pol1)

plot(x,y)
lines(x, f1(x), col = 2)

Clearly, this model appears insufficient. Therefore I intended to aplly
fit2 = lm(y ~ I(1/x))
pol2 = polynomial(fit2$coefficients)
f2 = as.function(pol2)
lines(x, f2(x), col = 3)

as this would be much more pleasant. However, the second model does not work
at all.


Does anyone know about how to correctly fit an x^-1-polynomial to my data
cloud?


Many thanks in advance,


behelfsadresse

	[[alternative HTML version deleted]]

Hi

r-help-bounces at r-project.org napsal dne 07.06.2010 14:28:58:
> Dear list,
> 
> I am getting weired with fitting data with a 1/x-polynomial. Suggest I 
have
> the following data:
> 
> x <- c(1,2,3,4,5,6,7)
> y <- c(100,20,4,2,1,.3,.1)
> 
> I may fit this with a linear model
> 
> fit1 = lm(y ~ I(x))
fit1 = lm(y ~ x)
is enough
> 
> Getting plot out of this model I applied
> library(polynom)
> pol1 = polynomial(fit1$coefficients)
> f1 = as.function(pol1)
> 
> plot(x,y)
> lines(x, f1(x), col = 2)
why not

plot(x,y)
lines(x, fitted(fit))

> 
> Clearly, this model appears insufficient. Therefore I intended to aplly
> fit2 = lm(y ~ I(1/x))
> pol2 = polynomial(fit2$coefficients)
> f2 = as.function(pol2)
> lines(x, f2(x), col = 3)
The same applies here

fit3 = lm(y ~ I(1/x^3))
lines(x, fitted(fit3))

seems to give quite reasonable output.

Regards
Petr
> 
> as this would be much more pleasant. However, the second model does not 
work
> at all.
> 
> 
> Does anyone know about how to correctly fit an x^-1-polynomial to my 
data
> cloud?
> 
> 
> Many thanks in advance,
> 
> 
> behelfsadresse
> 
>    [[alternative HTML version deleted]]
> 
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