R help - Jun 2006 - Intercept of confidence interval with a constant

Hello,

Is there a way for R to determine the point where a confidence interval equals 
a specified value? For example:

x = seq(1:5)
y = c(5, 5, 4, 4, 3)
lm = lm(y ~ x)
p = predict.lm(lm, interval="confidence")
matplot(p, type="b")
abline(h = 3)

I want to answer the question: "What is the value of x when the y-value of
the
lower confidence interval is equal to 3.0"? Visually, it is the place on
the
example where the abline intersects the lower confidence interval, or about 
4.2. Can R calculate this number for me?

I know that predict.lm will calculate a y-value from an x-value, but what I 
want is the opposite. I know the y-value, and I want to calculate the 
x-value.

Larry Howe

Try this:

approx(p[,"lwr"], 1:5, 3)

On 6/2/06, Larry Howe <linux at comjet.com> wrote:
> Hello,
>
> Is there a way for R to determine the point where a confidence interval
equals
> a specified value? For example:
>
> x = seq(1:5)
> y = c(5, 5, 4, 4, 3)
> lm = lm(y ~ x)
> p = predict.lm(lm, interval="confidence")
> matplot(p, type="b")
> abline(h = 3)
>
> I want to answer the question: "What is the value of x when the
y-value of the
> lower confidence interval is equal to 3.0"? Visually, it is the place
on the
> example where the abline intersects the lower confidence interval, or about
> 4.2. Can R calculate this number for me?
>
> I know that predict.lm will calculate a y-value from an x-value, but what I
> want is the opposite. I know the y-value, and I want to calculate the
> x-value.
>
> Larry Howe
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html
>

Larry Howe wrote:
> Hello,
> 
> Is there a way for R to determine the point where a confidence interval
equals
> a specified value? For example:
> 
> x = seq(1:5)
> y = c(5, 5, 4, 4, 3)
> lm = lm(y ~ x)
> p = predict.lm(lm, interval="confidence")
> matplot(p, type="b")
> abline(h = 3)

You can do it this way:

  optimize(function(x)
            (predict(lm, newdata = data.frame(x=x),
                     interval = "confidence")[,2] - 3)^2,
           interval=c(1, 5))$minimum

but maybe you are going to solve a "calibration" problem, in fact and
a
completely different kind of confidence interval (namely for the x-axis)?


Uwe Ligges

> I want to answer the question: "What is the value of x when the
y-value of the
> lower confidence interval is equal to 3.0"? Visually, it is the place
on the
> example where the abline intersects the lower confidence interval, or about
> 4.2. Can R calculate this number for me?
> 
> I know that predict.lm will calculate a y-value from an x-value, but what I
> want is the opposite. I know the y-value, and I want to calculate the 
> x-value.
> 
> Larry Howe
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide!
http://www.R-project.org/posting-guide.html

Ah, so I switch y with x, give it x, and ask it for y (which is actually x). 
Clever.

I continue to be impressed with R.

Thanks, Larry

On Friday June 2 2006 11:23, Gabor Grothendieck wrote:
> Try this:
>
> approx(p[,"lwr"], 1:5, 3)
>
> On 6/2/06, Larry Howe <linux at comjet.com> wrote:
> > Hello,
> >
> > Is there a way for R to determine the point where a confidence
interval
> > equals a specified value? For example:
> >
> > x = seq(1:5)
> > y = c(5, 5, 4, 4, 3)
> > lm = lm(y ~ x)
> > p = predict.lm(lm, interval="confidence")
> > matplot(p, type="b")
> > abline(h = 3)
> >
> > I want to answer the question: "What is the value of x when the
y-value
> > of the lower confidence interval is equal to 3.0"? Visually, it
is the
> > place on the example where the abline intersects the lower confidence
> > interval, or about 4.2. Can R calculate this number for me?
> >
> > I know that predict.lm will calculate a y-value from an x-value, but
what
> > I want is the opposite. I know the y-value, and I want to calculate
the
> > x-value.
> >
> > Larry Howe
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide!
> > http://www.R-project.org/posting-guide.html