How to predict x values from a linear model (lm)

Question

I have this data set:

x <- c(0, 40, 80, 120, 160, 200)
y <- c(6.52, 5.10, 4.43, 3.99, 3.75, 3.60)

I calculated a linear model using lm():

model <- lm(y ~ x)

I want know the predicted values of x if I have new y values, e.g. ynew <- c(5.5, 4.5, 3.5), but if I use the predict() function, it calculates only new y values.

How can I predict new x values if I have new y values?

Answer 1

Since this is a typical problem in chemistry (predict values from a calibration), package chemCal provides inverse.predict. However, this function is limited to "univariate model object[s] of class lm or rlm with model formula y ~ x or y ~ x - 1."

x <- c(0, 40, 80, 120, 160, 200)
y <- c(6.52, 5.10, 4.43, 3.99, 3.75, 3.60)
plot(x,y)
model <- lm(y ~ x)
abline(model)
require(chemCal)
ynew <- c(5.5, 4.5, 3.5)
xpred<-t(sapply(ynew,function(y) inverse.predict(model,y)[1:2]))
#  Prediction Standard Error
#[1,] 31.43007   -38.97289     
#[2,] 104.7669   -36.45131     
#[3,] 178.1037   -39.69539
points(xpred[,1],ynew,col="red")

Warning: This function is quite slow and not suitable, if you need to inverse.predict a large number of values.

If I remember correctly, the neg. SEs occur because the function expects the slope to be always positive. Absolute values of SE should still be correct.

Answer 2

I think you just have to use the algebra to invert y=a+b*x to x=(y-a)/b:

cc <- coef(model)
(xnew <- (ynew-cc[1])/cc[2])
# [1]  31.43007 104.76689 178.10372

plot(x,y
abline(model)
points(xnew,ynew,col=2)

Looking at your 'data' here, I think a nonlinear regression might be better ...