[R] within and between subject calculation

[Douglas Bates]

On 6/14/05, Kerry Bush <kerryrekky at yahoo.com> wrote:
> Dear helpers in this forum,
> 
> I have the following question:
> 
> Suppose I have the following data set:
> 
> id x y
> 023 1 2
> 023 2 5
> 023 4 6
> 023 5 7
> 412 2 5
> 412 3 4
> 412 4 6
> 412 7 9
> 220 5 7
> 220 4 8
> 220 9 8
> ......
> 
> and i want to calculate sum_{i=1}^k
> sum_{j=1}^{n_i}x_{ij}*y_{ij}
> 
> is there a simple way to do this within and between
> subject summation in R?

You didn't make it clear what the indices i and j refer to.  It seems
that part of the answer could use

> samp
    id x y
1   23 1 2
2   23 2 5
3   23 4 6
4   23 5 7
5  412 2 5
6  412 3 4
7  412 4 6
8  412 7 9
9  220 5 7
10 220 4 8
11 220 9 8
> with(samp, tapply(x*y, id, sum))
 23 220 412 
 71 139 109 

but if you then sum this result you simply get the sum of x * y.