[R] How to predict intersection value between regression and line in R?

[Luigi Marongiu]

I am trying to predict the intersection value between a curve and a line.
I can fit a logistic model to the data by converting the data to the
range 0-1. How can I determine the intersection with a line?
Also, is there a way to do the same without converting the data?
Here is an example:

```
val = c(120.64,    66.14,    34.87,    27.11,    8.87,    -5.8,
4.52,    -7.16,    -17.39,
       -14.29,    -20.26,    -14.99,    -21.05,    -20.64,    -8.03,
 -21.56,    -1.28,    15.01,
       75.26,    191.76,    455.09,    985.96,    1825.59,    2908.08,
   3993.18,    5059.94,
       6071.93,    6986.32,    7796.01,    8502.25,    9111.46,
9638.01,    10077.19,
       10452.02,    10751.81,    11017.49,    11240.37,    11427.47,
 11570.07,    11684.96,
       11781.77,    11863.35,    11927.44,    11980.81,    12021.88,
 12058.35,    12100.63,
       12133.57,    12148.89,    12137.09)
df = data.frame(Cycles = 1:35, Values = val[1:cyc])
M = max(df$Values)
df$Norm = df$Values/M
df$Norm[df$Norm<0] = 0
b_model = glm(Norm ~ Cycles, data=df, family=binomial)
x = 0.15
plot(Norm ~ Cycles, df, main="Normalized view",
     xlab=expression(bold("Amplification cycle")),
     ylab=expression(bold("Fluorescence (normalized)")),
     type="l", lwd=3, col="blue")
lines(b_model$fitted.values ~ df$Cycles, col="red", lwd=2, lty=2)
abline(h=x, col="green", lwd=2)
```
Thank you