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

[Kevin J Emerson]

Hello all,

This is something that I am sure has a really suave solution in R, but I can't quite figure out the best (or even a basic) way to do it.

I have a simple linear regression that is fit with lm for which I would like to estimate the x intercept with some measure of error around it (confidence interval).  In biology, there is the concept of a developmental zero - a temperature under which development will not happen. This is often estimated by extrapolation of a curve of developmental rate as a function of temperature.  This developmental zero is generally reported without error.  I intend to change this!  There has to be some way to assign error to this term, I just have yet to figure it out.

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.  

I would greatly appreciate any insight you may be able to share.

Cheers,
Kevin

Here is a small representative sample of some of my data where Dev.Rate ~ Temperature.

t <-
structure(list(Temperature = c(5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 
5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 10.5, 
10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 10.5, 
10.5, 10.5, 10.5, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 
12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 16, 16, 16, 16, 16, 
16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 18, 18, 
18, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 
20, 20, 22, 22), Dev.Rate = c(0.007518797, 0.007518797, 0.007518797, 
0.007194245, 0.007194245, 0.007194245, 0.007194245, 0.007194245, 
0.007194245, 0.006896552, 0.006896552, 0.012820513, 0.012820513, 
0.012195122, 0.012195122, 0.012195122, 0.012195122, 0.011363636, 
0.011363636, 0.011363636, 0.011363636, 0.011363636, 0.011363636, 
0.011363636, 0.010869565, 0.00952381, 0.00952381, 0.015151515, 
0.015151515, 0.022727273, 0.022727273, 0.022727273, 0.022727273, 
0.022727273, 0.022727273, 0.022727273, 0.022727273, 0.022727273, 
0.022727273, 0.022727273, 0.022727273, 0.020833333, 0.020833333, 
0.020833333, 0.034482759, 0.029411765, 0.029411765, 0.029411765, 
0.029411765, 0.029411765, 0.029411765, 0.029411765, 0.029411765, 
0.029411765, 0.029411765, 0.029411765, 0.029411765, 0.029411765, 
0.029411765, 0.029411765, 0.027027027, 0.025, 0.038461538, 0.03030303, 
0.03030303, 0.03030303, 0.052631579, 0.052631579, 0.045454545, 
0.045454545, 0.045454545, 0.045454545, 0.045454545, 0.045454545, 
0.045454545, 0.045454545, 0.045454545, 0.038461538, 0.038461538, 
0.038461538, 0.038461538, 0.038461538, 0.038461538, 0.038461538, 
0.038461538, 0.047619048, 0.047619048, 0.047619048, 0.047619048, 
0.047619048, 0.0625, 0.0625, 0.0625, 0.0625, 0.0625, 0.0625, 
0.0625, 0.0625, 0.0625, 0.0625, 0.052631579, 0.052631579, 0.052631579, 
0.052631579, 0.052631579, 0.076923077, 0.071428571)), .Names = c("Temperature", 
"Dev.Rate"), class = "data.frame", row.names = c(NA, 107L))



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Kevin J Emerson
Bradshaw-Holzapfel Lab
Center for Ecology and Evolutionary Biology
1210 University of Oregon
Eugene, Oregon 97403
kemerson at uoregon.edu