From: R. Michael Weylandt <michael.weylandt_at_gmail.com>

Date: Tue, 22 May 2012 12:30:47 -0400

R-help_at_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. Received on Tue 22 May 2012 - 16:34:25 GMT

Date: Tue, 22 May 2012 12:30:47 -0400

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.,

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_at_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_at_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_at_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_at_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_at_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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