# p-value for the fitted parameters in linear models

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## p-value for the fitted parameters in linear models

 Hi All, when using the linear model lm() to fit data of the form y = k * x + b, is it possible to know the p-value for the parameters k and b? i.e. can we find the result of the form (k, Δk; b, Δb)? Thanks in advance! Li Sun ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: p-value for the fitted parameters in linear models

 On 24.06.2012 17:47, Li SUN wrote: > Hi All, > > when using the linear model lm() to fit data of the form y = k * x + > b, is it possible to know the p-value for the parameters k and b? i.e. > can we find the result of the form (k, Δk; b, Δb)? If you explain what Δk means in a linear model, we may be able to help. Also, what is "the p-value of the parameters"? Obviously a hypothesis is missing in this sentence. Best, Uwe Ligges > > Thanks in advance! > > Li Sun > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: p-value for the fitted parameters in linear models

 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? Li Sun 2012/6/24 Uwe Ligges <[hidden email]>: > > > On 24.06.2012 17:47, Li SUN wrote: >> >> Hi All, >> >> when using the linear model lm() to fit data of the form y = k * x + >> b, is it possible to know the p-value for the parameters k and b? i.e. >> can we find the result of the form (k, Δk; b, Δb)? > > > If you explain what Δk means in a linear model, we may be able to help. > Also, what is "the p-value of the parameters"? Obviously a hypothesis is > missing in this sentence. > > Best, > Uwe Ligges > > > > >> >> Thanks in advance! >> >> Li Sun >> >> ______________________________________________ >> [hidden email] mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help>> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html>> and provide commented, minimal, self-contained, reproducible code. >> > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: p-value for the fitted parameters in linear models

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## Re: p-value for the fitted parameters in linear models

 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,                  [hidden email] 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 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: p-value for the fitted parameters in linear models

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## Re: p-value for the fitted parameters in linear models

 In reply to this post by Uwe Ligges-3 >> But what if x is exact while y has some uncertainty Δy, in the >> relation y = k * x + b? > >Again, no: this is not a linear model. Assumption in a linear model is >that the errors are identically distributed. Surely not; errors in a linear model do not need to be homoscedastic. lm handles heteroscadasticity in y via weights, and the formulation above looks  to be simply a linear model with heteroscedastic error in y. What lm will _not_ do is fit the fixed effects model taking acount _solely_ of the 'uncertainties' in x. It will use the weighted sum of squared residuals, and although that is the usual thing to do it may not be what the OP wants. But since the OP first asked about fitting with error in x one might suspect there is more to it; if this is just the original question turned round, the answer would be that turning the regression round is only sensible when y was the predictor in the first place - in which case the original question was the wrong way round. And if the OP is now simply ignoring error in x that is actually present, that too would speak against simple linear regression. Those are pretty fundamental issues, so finding a local statistician is indeed the only safe course. S Ellison ******************************************************************* This email and any attachments are confidential. Any use...{{dropped:8}} ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.