Question

I have two linear fits that I’ve gotten from lm calls in my R script. For instance…

fit1 <- lm(y1 ~ x1)
fit2 <- lm(y2 ~ x2)

I’d like to find the (x,y) point at which these two lines (fit1 and fit2) intersect, if they intersect at all.

Answer 1

One way to avoid the geometry is to re-parameterize the equations as:

y1 = m1 * (x1 - x0) + y0
y2 = m2 * (x2 - x0) + y0

in terms of their intersection point (x0, y0) and then perform the fit of both at once using nls so that the returned values of x0 and y0 give the result:

# test data
set.seed(123)
x1 <- 1:10
y1 <- -5 + x1 + rnorm(10)
x2 <- 1:10
y2 <- 5 - x1 + rnorm(10)
g <- rep(1:2, each = 10) # first 10 are from x1,y1 and second 10 are from x2,y2

xx <- c(x1, x2)
yy <- c(y1, y2)
nls(yy ~ ifelse(g == 1, m1 * (xx - x0) + y0, m2 * (xx - x0) + y0),
    start = c(m1 = -1, m2 = 1, y0 = 0, x0 = 0))

EDIT: Note that the lines xx<-... and yy<-... are new and the nls line has been specified in terms of those and corrected.