[R] confidence interval or error of x intercept of a linear regression

Thomas Lumley tlumley at u.washington.edu
Tue Mar 24 09:15:15 CET 2009

On Mon, 23 Mar 2009, Kevin J Emerson wrote:

> Now, it is simple enough to calculate the x-intercept itself ( - intercept / 
> slope ), but it is a whole separate process to generate the confidence 
> interval of it.  I can't figure out how to propagate the error of the slope 
> and intercept into the ratio of the two.  The option option I have tried to 
> figure out is to use the predict function to look for where the confidence 
> intervals cross the axis but this hasn't been too fruitful either.

A few people have written code to do nonlinear transformations automatically. 
There's one in my 'survey' package, and I think there's an example in Venables 
& Ripley's "S Programming", and I'm sure there are others.

For example
> library(survey)
> m<-lm(Dev.Rate~Temperature, data=t)
> svycontrast(m, quote(-`(Intercept)`/Temperature))
          nlcon     SE
contrast 3.8061  0.1975

The `backquotes` are necessary because the coefficient name, (Intercept), isn't a legal variable name.

The svycontrast() function works on anything that has coef() and vcov() methods. The actual delta-method computations are in survey:::nlcon


Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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