[R] Weighted least squares

Wed May 9 02:37:31 CEST 2007

```http://en.wikipedia.org/wiki/Weighted_least_squares gives a formulaic
description of what you have said.

I believe the original poster has converted something like this

y	  x
0	1.1
0	2.2
0	2.2
0	2.2
1	3.3
1	3.3
2	4.4
...

into something like the following

y	  x	freq
0	1.1	   1
0	2.2	   3
1	3.3        2
2	4.4        1
...

Now, the variance of means of each row in table above is ZERO because
the individual elements that comprise each row are identical. Therefore
your method of using inverse-variance will not work here.

Then is it valid then to use lm( y ~ x, weights=freq ) ?

S Ellison wrote:
>
>> .. what is the usual way to do a linear
>> regression when you have aggregated data?
>
> Least squares generally uses inverse variance weighting. For aggregated data fitted as mean values, you just need the variances for the _means_.
>
> So if you have individual means x_i and sd's s_i that arise from aggregated data with n_i observations in group i, the natural weighting is by inverse squared standard error of the mean. The appropriate weight for x_i would then be n_i/(s_i^2). In R, that's n/(s^2), as n and s would be vectors with the same length as x. If all the groups had the same variance, or nearly so, s is a scalar; if they have the same number of observations, n is a scalar.
>
> Of course, if they have the same variance and same number of observations, they all have the same weight and you needn't weight them at all: see previous posting!
>
> Steve E
>
>
>
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