[R] How to get a given cut-off in logit regression?

[Luigi Marongiu]

Hello,
I would like to calculate the 95% success rate of a test. I have a
series of dilutions and the proportion of positive results out of 37
attempts for each of them. I would like to find the concentration that
gives 95% success and I used logit regression:
```
df <- data.frame(concentration = c(1, 10, 100, 1000, 10000),
positivity = c(0.86, 1, 1, 1, 1))
model <- glm(positivity~concentration, family="binomial", data=df)
summary(model)
confint(model)
```
When running the model, I get a warning:
```
Warning messages:
1: In eval(family$initialize) : non-integer #successes in a binomial glm!
2: glm.fit: algorithm did not converge
3: glm.fit: fitted probabilities numerically 0 or 1 occurred
```
but I got  something:
```
> summary(model)

Call:
glm(formula = positivity ~ concentration, family = "binomial",
data = df)

Deviance Residuals:
1         2         3         4         5
0.00e+00  4.41e-04  2.00e-08  2.00e-08  2.00e-08

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)      0.223    216.154   0.001    0.999
concentration    1.592    216.131   0.007    0.994

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 4.6727e-01  on 4  degrees of freedom
Residual deviance: 1.9445e-07  on 3  degrees of freedom
AIC: 4.3016

Number of Fisher Scoring iterations: 25
```

How can I now find the concentration that gives 95% positivity?

Thanks

-- 
Best regards,
Luigi