[R] weighted regression

[Thomas W Blackwell]

Rex  -

Yes, you have supplied an appropriate 'weight' argument
given the problem description in the paragraph which
begins 'Assume that ...'.

Your example would be much easier to read if the variable
names 'x' and 'y' in the R code matched their usage in the
paragraph description, rather than transposing.  But the
usage within the R code is consistent, although counter-
intuitive.  Your example tries to predict the values of
an almost constant vector c(6.7,6.7,6.6) from a highly
varying one, c(1,6,11).  No surprise that the intercept
with the vertical axis is a bit larger than 6.7 and the
slope is completely non-significant.

-  tom blackwell  -  u michigan medical school  -  ann arbor  =

On Thu, 18 Dec 2003, rex_bryan at urscorp.com wrote:

> To all
>
> I have some simple questions pertaining to weights used in regression.
> If the variability of the dependent variable (y) is a function of the magnitude of predictor
> variable (x), can the use of weights give an appropriate answer to the regression parameters
> and the std errors?
>
> Assume that y at x=1 and 6 has a standard deviation of 0.1 and at x=11 it is 0.4
> Then according to a web page on weighted regression for a calibration curve at
> http://member.nifty.ne.jp/mniwa/rev006.htm, I should use 1/(std^2) for each weight.
>
> i.e. for x=1 and 6, w = 100 and x=11, w = 6.25
>
> In R the run is:
>
> >y<-c(1,6,11)
> >x<-c(6.7,6.7,6.6)
> >w<-c(100,100,6.25)
> >reg <-lm(x~y, weight=w)
> > summary(reg)
>
> Call:
> lm(formula = x ~ y, weights = w)
>
> Residuals:
>        1        2        3
> -0.04762  0.09524 -0.19048
>
> Coefficients:
>              Estimate Std. Error t value Pr(>|t|)
> (Intercept)  6.707619   0.025431 263.762  0.00241 **
> y           -0.002857   0.005471  -0.522  0.69361
> ---
> Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1
>
> Residual standard error: 0.2182 on 1 degrees of freedom
> Multiple R-Squared: 0.2143,     Adjusted R-squared: -0.5714
> F-statistic: 0.2727 on 1 and 1 DF,  p-value: 0.6936
>
> Am I using the weight method correctly?
> And if so does the Estimated Std. Error for the Intercept and slope make sense?
>
> On another note.  How does one do a regression with the origin fixed at 0?
>
> Merry Christmas
>
> REX
>
>
>
>
>
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>
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