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

[Duncan Murdoch]

Your example doesn't run because it uses a variable `cyc` which you 
didn't include.

But in general, I think you are mixing up two separate problems here.

The first problem is creating a function of x (which is Cycles in your 
dataset).  You used the predictions from a glm() to do this.

That's a reasonable way to create a function with a range of 0 to 1, but 
you want a function with a different range.  Dividing by the max is one 
way to get it, but there are others.  I'd say a better approach would be 
to think about the problem from a subject matter point of view and 
determine a class of functions that match your needs.  After you've done 
that, you might use glm() to find the particular version of that 
function (i.e. the unknown parameters), or maybe some other method.

The second problem is finding where that function intersects a line.  In 
your sample code, you were trying to intersect a horizontal line.  If 
that's always the case, then it's a problem of inverting the function 
from the first problem.  Just write out y = f(x) and solve for x = 
f^-1(y).  If the formula isn't convenient, you can approximate the 
answer using the R function uniroot().

Duncan Murdoch

On 2025-04-11 11:53 a.m., Luigi Marongiu wrote:
> 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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