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

[Uwe Ligges]

On 24.06.2012 20:35, Li SUN wrote:
> 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?

Again, no: this is not a linear model. Assumption in a linear model is 
that the errors are identically distributed.

Uwe Ligges



>
>
> 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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>
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>