From: Adaikalavan Ramasamy <ramasamy_at_cancer.org.uk>

Date: Wed, 09 May 2007 01:37:31 +0100

R-help_at_stat.math.ethz.ch 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 Wed 09 May 2007 - 00:43:35 GMT

Date: Wed, 09 May 2007 01:37:31 +0100

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 ...

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

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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**> ______________________________________________
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**> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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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 Wed 09 May 2007 - 00:43:35 GMT

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