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