Calibration (inverse prediction) from LOESS object

I have fit a LOESS local regression to some data and I want to be able to find the X value associated with a given Y value.

plot(cars, main = "Stopping Distance versus Speed")
car_loess <- loess(cars$dist~cars$speed,span=.5)
lines(1:50, predict(car_loess,data.frame(speed=1:50)))

I was hoping that I could use teh inverse.predict function from the chemCal package, but that does not work for LOESS objects.

Does anyone have any idea how I might be able to do this calibrationa in a better way than predicticting Y values from a long vector of X values and looking through the resulting fitted Y for the Y value of interest and taking its corresponding X value?

Practically speaking in the above example, let's say I wanted to find the speed at which the stopping distance is 15.

Thanks!

The predicted line that you added to the plot is not quite right. Use code like this instead:

# plot the loess line
lines(cars$speed, car_loess$fitted, col="red")

You can use the approx() function to get a linear approximation from the loess line at a give y value. It works just fine for the example that you give:

# define a given y value at which you wish to approximate x from the loess line
givenY <- 15
estX <- approx(x=car_loess$fitted, y=car_loess$x, xout=givenY)$y
# add corresponding lines to the plot
abline(h=givenY, lty=2)
abline(v=estX, lty=2)

But, with a loess fit, there may be more than one x for a given y. The approach I am suggesting does not provide you with ALL of the x values for the given y. For example ...

# example with non-monotonic x-y relation
y <- c(1:20, 19:1, 2:20)
x <- seq(y)
plot(x, y)
fit <- loess(y ~ x)
# plot the loess line
lines(x, fit$fitted, col="red")

# define a given y value at which you wish to approximate x from the loess line
givenY <- 15
estX <- approx(x=fit$fitted, y=fit$x, xout=givenY)$y
# add corresponding lines to the plot
abline(h=givenY, lty=2)
abline(v=estX, lty=2)