LM with summation function

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 at 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 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]]

? ? ? ?[[alternative HTML version deleted]]

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 at 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 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]]

	[[alternative HTML version deleted]]