You can try this:
library(inflection)
#you have to instsall package inflection first
a<-findiplist(cbind(year),cbind(piproute),1)
a
The answer:
[,1] [,2] [,3]
[1,] 5 35 1986.0
[2,] 5 30 1983.5
shows that the total inflection point is between 1983 and 1986, if we treat
data as first concave and then convex, as it can be found from a simple
graph.
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