R's lm(), get x when y is known

Question

Here is some data and a logarithmic model:

df <- data.frame(
  x = 1:8,
  y = c(7.5,6,5.2,4.3,3.9,3.4,3.1,2.9)
)

model <- lm(y ~ log(x), data = df)

I am able to use this model to predict y for any given x e.g.

predict(model, newdata = data.frame(x = 10)) # 2.3

My question is, if I want to find y when x is known, can I do that? 'Reverse prediction' or what's the correct term?

e.g. If I want to know the value of x when the function output is 8, how would I do that?

I'm assuming that whoever closed this pasted the wrong duplicate link, because I don't see how that linked post answers the question. — Doug Fir, Apr 09 '21 at 17:23

score 1 · Answer 1 · answered Apr 09 '21 at 11:31

1

I don't have enough reputation to comment, but I've heard it referred to as calibration or inverse regression. Hope that gives you something to start.

answered Apr 09 '21 at 11:31

PRZ

113
4

Thanks for the info @PRZ! – Doug Fir Apr 09 '21 at 11:41

score 1 · Accepted Answer · answered Apr 09 '21 at 11:42

1

In your specific case

Coefficients:
(Intercept)       log(x)  
      7.544       -2.268

In original

$$y=7.544-2.268 \cdot \log(x)$$

therefore

$$(7.544 - y)/2.268 = \log(x)$$

or

$$\exp((7.544 - y)/2.268) = x$$

answered Apr 09 '21 at 11:42

user2974951

5,700
2
14
27

R's lm(), get x when y is known

2 Answers2