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]>
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