# How to I find out where the lower bounds of a tolerance interval crosses a given threshold?

Suppose I have some data:

y<-c(10, 5, 2, 0, 2, 4, 9)
x<-c(-3,-2, -1, 0, 1, 2, 3)


And I want to fit a curve to the data and get a tolerance interval

mylm <- lm(y~poly(x,2,raw=TRUE))
ti <- regtol.int(reg = mylm, new.x = NULL, alpha = 0.1, P = 0.80, side = 2)


I want to determine for my calculated tolerance interval, for what values of x am I going to have y values below the lower bound?

Here's the plotted values, for reference:

plottol(ti,x=poly(x,2,raw=TRUE),y=y,side="lower",x.lab="x",y.lab="y")


So, in my example, I want a y value of at least 4 (so I am only concerned with the lower limit) and I want to find out that I need an x value of less than 2, or greater than two.

Another way of asking my question is, "how can I find every value where the lower tolerance limit crosses a given threshold"?

In reality my data is almost linear (I could get away without using a polynomial) so if that substantially simplifies the problem, I could probably live with it.

On a side note, my plot gives this error:

In if (class(tol.out) == "list" & is.null(names(tol.out)) == FALSE &  :
the condition has length > 1 and only the first element will be used


Any idea what's causing that?

Thanks!

P.S. I've been thinking - if I could get line up the factor values with the values returned by regtol.int, then I could fit a line to the limits - maybe kludgy, but it would work. But R, behind the scenes, is already doing this when I call plottol... for the life of my I can't figure out where.

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