[R] graphing repeated curves

[Bert Gunter]

I do not think this does what the OP wants -- it does not produce
polynomials of the form desired.

John Fox's solution using poly() seems to me to be the right approach, but
I will show what I think is a considerably simpler way to build up the
polynomial expressions just as an example of one way to do this sort of
thing in more general circumstances:

fm <- vector("character",6)
fm[1]<- "mpg ~ hp"
for(i in 2:6)fm[i]<- paste0(fm[i-1]," + I(hp^", i,")")
## yielding:
> fm
[1] "mpg ~ hp"
[2] "mpg ~ hp + I(hp^2)"
[3] "mpg ~ hp + I(hp^2) + I(hp^3)"
[4] "mpg ~ hp + I(hp^2) + I(hp^3) + I(hp^4)"
[5] "mpg ~ hp + I(hp^2) + I(hp^3) + I(hp^4) + I(hp^5)"
[6] "mpg ~ hp + I(hp^2) + I(hp^3) + I(hp^4) + I(hp^5) + I(hp^6)"

Although fm is a character vector, the character strings will be
automatically coerced by lm to formulas (see ?lm), so, e.g.

results <- lapply(fm, lm,data = mtcars)

would yield a list of regressions which could then be summarized, plotted
or whatever (again using lapply). e.g.

> results[[3]]

Call:
FUN(formula = X[[i]], data = ..1)

Coefficients:
(Intercept)           hp      I(hp^2)      I(hp^3)
  4.422e+01   -2.945e-01    9.115e-04   -8.701e-07

One could also choose to do the plotting or whatever within the lapply
call, but I prefer to keep things simple if possible.

Cheers,
Bert



Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Wed, Aug 22, 2018 at 4:43 PM Jim Lemon <drjimlemon using gmail.com> wrote:

> Hi Richard,
> This may be what you want:
>
> data(mtcars)
> m<-list()
> for(i in 1:6) {
>  rhterms<-paste(paste0("I(hp^",1:i,")"),sep="+")
>  lmexp<-paste0("lm(mpg~",rhterms,",mtcars)")
>  cat(lmexp,"\n")
>  m[[i]]<-eval(parse(text=lmexp))
> }
> plot(mpg~hp,mtcars,type="n")
> for(i in 1:6) abline(m[[i]],col=i)
>
> Jim
>
>
> On Thu, Aug 23, 2018 at 9:07 AM, Richard Sherman <rss.pdx using gmail.com>
> wrote:
> > Hi all,
> >
> > I have a simple graphing question that is not really a graphing
> question, but a question about repeating a task.
> >
> > I’m fiddling with some of McElreath’s Statistical Rethinking, and
> there’s a graph illustrating extreme overfitting (a number of polynomial
> terms in x equal to the number of observations), a subject I know well
> having taught it to grad students for many years.
> >
> > The plot I want to reproduce has, in effect:
> >
> > m1 <- lm( y ~ x)
> > m2 <- lm( y ~ x + x^2)
> >
> > …etc., through lm( y ~ x + x^2 + x^3 + x^4 + x^5 + x^6 ), followed by
> some plot() or lines() or ggplot2() call to render the data and fitted
> curves.
> >
> > Obviously I don’t want to run such regressions for any real purpose, but
> I think it might be useful to learn how to do such a thing in R without
> writing down each lm() call individually. It’s not obvious where I’d want
> to apply this, but I like learning how to repeat things in a compact way.
> >
> > So, something like:
> >
> > data( mtcars )
> > d <- mtcars
> > v <- c( 1 , 2 , 3 , 4 , 5 , 6  )
> > m1 <- lm( mpg ~ hp  , data = d )
> >
> > and then somehow use for() with an index or some flavor of apply() with
> the vector v to repeat this process yielding
> >
> > m2 <- lm( mpg ~ hp + I( hp ^2 ) , data=d)
> > m3 <- lm( mpg ~ hp + I( hp^2 ) + I(hp^3) , data=d )
> >
> > … and the rest through m6 <- lm( mpg ~ hp + I(hp^2) + I(hp^3) + I(hp^4)
> + I(hp^5) + I(hp^6) , data=d )
> >
> > But finding a way to index these values including not just each value
> but each value+1 , then value+1 and value+2, and so on escapes me.
> Obviously I don’t want to include index values below zero.
> >
> > ===
> > Richard Sherman
> > rss.pdx using gmail.com
> >
> > ______________________________________________
> > R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > 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 using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> 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.
>

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