# [R] How to find the interception point of two linear fitted model in R?

Paul Johnson pauljohn32 at gmail.com
Wed Oct 21 19:18:17 CEST 2009

```On Wed, Oct 21, 2009 at 12:09 PM, FMH <kagba2006 at yahoo.com> wrote:
> Dear All,
>
> Let have 10 pair of observations, as shown below.
>
> ######################
> x <- 1:10
> y <- c(1,3,2,4,5,10,13,15,19,22)
> plot(x,y)
> ######################
>
>
> Two fitted  models, with ranges of [1,5] and [5,10], can be easily fitted separately by lm function as shown below:
>
> #######################
> mod1 <- lm(y[1:5] ~ x[1:5])
> mod2 <- lm(y[5:10] ~ x[5:10])
> #######################
>
> I'm looking for the interception points between these two straight lines from these fitted models, mod1 and mod2.
>
> Could someone advice me the way to do it?
>
> Thank you
> Fir

extract the coefficients, rearrange in a linear system, use solve.

>
> m1 <- as.matrix(rbind(coef(mod1), coef(mod2)))
> a <- cbind(c(1,1), -m1[, 2])
> a
[,1]      [,2]
[1,]    1 -0.900000
[2,]    1 -3.257143
> b <- m1[,1]
> solve(a=a,b=b)
[1] 4.396364 4.551515

This seems to "visually verify" the result:

> plot(1:10,1:10, type="n")
> abline(mod1)
> abline(mod2)

--
Paul E. Johnson
Professor, Political Science
1541 Lilac Lane, Room 504
University of Kansas

```