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

[Li SUN]

Thanks David and Brian.

But what if x is exact while y has some uncertainty Δy, in the
relation y = k * x + b?

Now I need to fit some data like
x       = 1,          2,          3,          4,          5
y±Δy = 1.1±0.1, 2.0±0.2, 3.1±0.2, 4.1±0.1, 5.0±0.2

Is there any mechanism to pass x, y and Δy to lm() so that I can find
k, b as well as their uncertainties Δk, Δb?


Li Sun


2012/6/24 Prof Brian Ripley <ripley at stats.ox.ac.uk>:
> 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
>
>
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