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: [EMAIL PROTECTED] -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] 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: [EMAIL PROTECTED]<mailto:[EMAIL PROTECTED]> > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@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. ______________________________________________ R-help@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.
