[R] p-value for the fitted parameters in linear models

[Prof Brian Ripley]

On 24/06/2012 18:39, David Winsemius wrote:
>
> On Jun 24, 2012, at 1:21 PM, Li SUN wrote:
>
>> Sorry for the confusion.
>>
>> Let me state the question again. I missed something in my original
>> statement.
>>
>> When using the linear model lm() to fit data of the form y = k * x +
>> b, where k, b are the coefficients to be found, and x is the variable
>> and has an error bar (uncertainty) Δx of the same length associated
>> with it. Is it possible to pass Δx to the linear model lm(), and from
>> the output to find the uncertainty Δk for k, Δb for b as well?
>
> In one sense this could be done if you were interpreting the "Δx" as the
> vector of individual residuals of a model, but I'm guessing that might
> not be what you meant. You would be able to recover the original data,
> assuming you knew the X values, and would proceed by calculating the Y
> values as the sum of predictions and the residuals, thus recovering the
> original data. But  I'm guessing you want to supply a small number of
> parameters from an analysis you are reading about and you are hoping to
> be getting from lm() further information to answer some question. That's
> not the direction of teh flow of information. The flow is data INTO
> lm(), estimation of parameters OUT.
>
> Show us a sample dataset constructed with R code or show us the console
> output of dput() applied to your dataset, and you may get better answers
> to what is still an unclear question.
>

This is not linear regression if 'x' is not known exactly.  There are 
various formulations of the problem, but that is off-topic here. 
However, consulting

@Book{Fuller.87,
   author       = "Fuller, Wayne A.",
   title        = "Measurement Error Models",
   publisher    = "John Wiley and Sons",
   address =      "New York",
   year         = "1987",
   ISBN         = "0-471-86187-1",
}

would be a good start.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595