[R] Weighted least squares

[Adaikalavan Ramasamy]

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 ) ?

Regards, Adai



S Ellison wrote:
> Hadley,
> 
> You asked
>> .. 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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