naive "collinear" weighted linear regression

Hi there

Sorry for what may be a naive or dumb question.

I have the following data:

x <- c(1,2,3,4) # predictor vector

y <- c(2,4,6,8) # response vector. Notice that it is an exact,  

perfect straight line through the origin and slope equal to 2

error <- c(0.3,0.3,0.3,0.3) # I have (equal) ``errors'', for  

instance, in the measured responses

Of course the best fit coefficients should be 0 for the intercept  
and 2 for the slope. Furthermore, it seems completely plausible (or  
not?) that, since the y_i have associated non-vanishing  
``errors'' (dispersions), there should be corresponding non- 
vanishing ``errors'' associated to the best fit coefficients, right?

When I try:

fit_mod <- lm(y~x,weights=1/error^2)

I get

Warning message:
In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
 extra arguments weigths are just disregarded.

Keeping on, despite the warning message, which I did not quite  
understand, when I type:

summary(fit_mod)

I get

Call:
lm(formula = y ~ x, weigths = 1/error^2)

Residuals:
        1          2          3          4
-5.067e-17  8.445e-17 -1.689e-17 -1.689e-17

Coefficients:
            Estimate Std. Error   t value Pr(>|t|)
(Intercept) 0.000e+00  8.776e-17 0.000e+00        1
x           2.000e+00  3.205e-17 6.241e+16   <2e-16 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Residual standard error: 7.166e-17 on 2 degrees of freedom
Multiple R-squared:     1,      Adjusted R-squared:     1
F-statistic: 3.895e+33 on 1 and 2 DF,  p-value: < 2.2e-16


Naively, should not the column Std. Error be different from zero??  
What I have in mind, and sure is not what Std. Error means, is that  
if I carried out a large simulation, assuming each response y_i a  
Gaussian random variable with mean y_i and standard deviation  
2*error=0.6, and then making an ordinary least squares fitting of  
the slope and intercept, I would end up with a mean for these  
simulated coefficients which should be 2 and 0, respectively,

and, that's the point, a non-vanishing standard deviation for these  
fitted coefficients, right?? This somehow is what I expected should  
be an estimate or, at least, a good indicator, of the degree of  
uncertainty which I should assign to the fitted coefficients; it  
seems to me these deviations, thus calculated as a result of the  
simulation, will certainly not be zero (or  3e-17, for that matter).  
So this Std. Error does not provide what I, naively, think should be  
given as a measure of the uncertainties or errors in the fitted  
coefficients...

What am I not getting right??

Thanks and sorry for the naive and non-expert question!

-- 
#######################################
Prof. Mauricio Ortiz Calvao
Federal University of Rio de Janeiro
Institute of Physics, P O Box 68528
CEP 21941-972 Rio de Janeiro, RJ
Brazil