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
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