I don't think I can.

For the sample data

 d <- data.frame(x=c(1, 4, 9, 12), s=c(109, 1200, 5325, 8216))

when x = 4, s = 1200.  However, that s4 is sum of y1 + y2 + y3 + y4.
 Wouldn't I have to know the y for x = 2 and x = 3 to get the value of y
for x = 4?

In the previous message, I created two sample data frames.  d is what I'm
trying to use to create df.  I only know what's in d, df is just used to
illustrate what I'm trying to get from d.

robbie





On Tue, May 22, 2012 at 12:30 PM, R. Michael Weylandt <
michael.weylandt@gmail.com> wrote:

> But if I understand your problem correctly, you can get the y values
> from the s values. I'm relying on your statement that "s is sum of the
> current y and all previous y (s3 = y1 + y2 + y3)." E.g.,
>
> y <- c(1, 4, 6, 9, 3, 7)
>
> s1 = 1
> s2 = 4 + s1 = 5
> s3 = 6 + s2 = 11
>
> more generally
>
> s <- cumsum(y)
>
> Then if we only see s, we can get back the y vector by doing
>
> c(s[1], diff(s))
>
> which is identical to y.
>
> So for your data, the underlying y must have been c(109, 1091, 4125,
> 2891) right?
>
> Or have I completely misunderstood your problem?
>
> Michael
>
> On Tue, May 22, 2012 at 12:25 PM, Robbie Edwards
> <robbie.edwards@gmail.com> wrote:
> > Actually, I can't.  I don't know the y values.  Only the s and only for a
> > subset of the data.
> >
> > Like this.
> >
> > d <- data.frame(x=c(1, 4, 9, 12), s=c(109, 1200, 5325, 8216))
> >
> >
> >
> > On Tue, May 22, 2012 at 11:57 AM, R. Michael Weylandt
> > <michael.weylandt@gmail.com> wrote:
> >>
> >> You can reconstruct the y values by taking first-differences of the s
> >> vector, no? Then it sounds like you're good to go
> >>
> >> Best, Michael
> >>
> >> On Tue, May 22, 2012 at 11:40 AM, Robbie Edwards
> >> <robbie.edwards@gmail.com> wrote:
> >> > Hi all,
> >> >
> >> > Thanks for the replies, but I realize I've done a bad job explaining
> my
> >> > problem.  To help, I've created some sample data to explain the
> problem.
> >> >
> >> > df <- data.frame(x=c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), y=c(109,
> >> > 232,
> >> > 363, 496, 625, 744, 847, 928, 981, 1000, 979, 912), s=c(109, 341, 704,
> >> > 1200, 1825, 2569, 3416, 4344, 5325, 6325, 7304, 8216))
> >> >
> >> > In this data frame, y results from y = x * b1 + x^2 * b2 + x^3 * b3
> and
> >> > s
> >> > is sum of the current y and all previous y (s3 = y1 + y2 + y3).
> >> >
> >> > I know I can find b1, b2 and b3 using:
> >> > lm(y ~ 0 + x + I(x^2) + I(x^3), data=df)
> >> >
> >> > yielding...
> >> > Coefficients:
> >> >     x  I(x^2)  I(x^3)
> >> >   100      10      -1
> >> >
> >> > However, I need to find b1, b2 and b3 using the s column.  The reason
> >> > being, I don't actually know the values of y in the actual data set.
> >> >  And
> >> > in the actual data, I only have a few of the values.  Imagine this
> data
> >> > is
> >> > being used a reward schedule for like a loyalty points program.  y
> >> > represents the number of points needed for each level while s is the
> >> > total
> >> > number of points to reach that level.  In the real problem, my data
> >> > looks
> >> > more like this:
> >> >
> >> > d <- data.frame(x=c(1, 4, 9, 12), s=c(109, 1200, 5325, 8216))
> >> >
> >> > Where I need to use a few sample points to help define the parameters
> of
> >> > the curve.
> >> >
> >> > thanks again and hopefully this makes the problem a bit clearer.
> >> >
> >> > robbie
> >> >
> >> >
> >> >
> >> > On Fri, May 18, 2012 at 7:40 PM, David Winsemius
> >> > <dwinsemius@comcast.net>wrote:
> >> >
> >> >>
> >> >> On May 18, 2012, at 1:44 PM, Robbie Edwards wrote:
> >> >>
> >> >>  Hi all,
> >> >>>
> >> >>> I'm trying to model some data where the y is defined by
> >> >>>
> >> >>> y = summation[1 to 50] B1 * x + B2 * x^2 + B3 * x^3
> >> >>>
> >> >>> Hopefully that reads clearly for email.
> >> >>>
> >> >>>
> >> >> cumsum( rowSums( cbind(B1 * x,  B2 * x^2, B3 * x^3)))
> >> >>
> >> >>
> >> >>
> >> >>  Anyway, if it wasn't for the summation, I know I would do it like
> this
> >> >>>
> >> >>> lm(y ~ x + x2 + x3)
> >> >>>
> >> >>> Where x2 and x3 are x^2 and x^3.
> >> >>>
> >> >>> However, since each value of x is related to the previous values of
> x,
> >> >>> I
> >> >>> don't know how to do this.  Any help is greatly appreciated.
> >> >>>
> >> >>>
> >> >>>
> >> >>
> >> >> David Winsemius, MD
> >> >> West Hartford, CT
> >> >>
> >> >>
> >> >
> >> >        [[alternative HTML version deleted]]
> >> >
> >> > ______________________________________________
> >> > R-help@r-project.org mailing list
> >> > 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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