From: Zhang Yanwei - Princeton-MRAm <YZhang_at_munichreamerica.com>

Date: Wed, 23 Jul 2008 15:46:17 -0400

R-help_at_r-project.org 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 23 Jul 2008 - 20:32:39 GMT

Date: Wed, 23 Jul 2008 15:46:17 -0400

I have figured out the problem. Thanks.

Sincerely,

Yanwei Zhang

Department of Actuarial Research and Modeling
Munich Re America

Tel: 609-275-2176

Email: yzhang_at_munichreamerica.com

-----Original Message-----

From: Zhang Yanwei - Princeton-MRAm

Sent: Wednesday, July 23, 2008 3:32 PM

To: Zhang Yanwei - Princeton-MRAm

Cc: r-help_at_r-project.org

Subject: RE: [R] Questions on weighted least squares

Sorry if I did not state clearly.

Put it another way. If the variance of the observation is proportional to the predictor, that is, var(y_i)=x_i*sigma^2, what should be specified in the "weights" argument in the lm function?
fit=lm(y~x,weights=???)

Sincerely,

Yanwei Zhang

Department of Actuarial Research and Modeling Munich Re America
Tel: 609-275-2176

Email: yzhang_at_munichreamerica.com

-----Original Message-----

From: markleeds_at_verizon.net [mailto:markleeds_at_verizon.net]
Sent: Wednesday, July 23, 2008 3:00 PM

To: Zhang Yanwei - Princeton-MRAm

Subject: RE: [R] Questions on weighted least squares

i'm not sure about your whole question but you shouldn't be normalizing the predictor. that i know. the predictors are considered "fixed" so there's no reason to normalize them, ever.

On Wed, Jul 23, 2008 at 2:49 PM, Zhang Yanwei - Princeton-MRAm wrote:

> Hi all,

*> I met with a problem about the weighted least square regression.
**> 1. I simulated a Normal vector (sim1) with mean 425906 and standard
**> deviation 40000.
**> 2. I simulated a second Normal vector with conditional mean b1*sim1,
**> where b1 is just a number I specified, and variance proportional to
**> sim1. Precisely, the standard deviation is sqrt(sim1)*50.
**> 3. Then I run a WLS regression without the intercept term with
**> "weights" equal to sqrt(sim1)*50. I wonder whether I should specify
**> the weights in this way so that each observation will have equal
**> variance 1.
**> 4. If step 3 is correct, it should yield the same result if I
**> normalize the response and the predictor first with sqrt(sim1)*50, and
**> then use the "lm" function without "weights". But the two methods
**> yield different results.
**> Would someone tell me which one is the correct way to do? Thanks in
**> advance, and the code and output are as follows:
**>
**>
**>> b1=474186/425906
**>> n=240
**>> sim1=rnorm(n,425906,40000)
**>> sim2=matrix(0,n,1)
**>> for (i in 1:(n)){
**> + sim2[i]=rnorm(1,sim1[i]*b1,sqrt(sim1[i])*50)
**> + }
**>> fit1=lm(sim2~-1+sim1,weights=sqrt(sim1)*50)
**>> coef(fit1)
**> sim1
**> 1.116028
**>> y=sim2/(sqrt(sim1)*50)
**>> x=sim1/(sqrt(sim1)*50)
**>> fit2=lm(y~-1+x)
**>> coef(fit2)
**> x
**> 1.116273
**>
**>
**> Sincerely,
**> Yanwei Zhang
**> Department of Actuarial Research and Modeling Munich Re America
**> Tel: 609-275-2176
**> Email: yzhang_at_munichreamerica.com<mailto:yzhang_at_munichreamerica.com>
**>
**>
**> [[alternative HTML version deleted]]
**>
**> ______________________________________________
**> R-help_at_r-project.org 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.
*

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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 23 Jul 2008 - 20:32:39 GMT

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