Simple Logistic Regression

jamesmartinn

Hello all, I've performed a simple logistic regression and could use some help in interpretations/minor calculations.

Five different doses of insecticide were applied under standardized conditions to samples of an insect species. The data were:

Dose: ---2.6---3.8---5.1---7.7---10.2---
Dead: ----7----16---20----48----54----
Total: ---60----60---59----57----60---

So I was asked to fit a logistic regression model that says the logit of chance of death increases linearly with the natural logarithm of dose (ml/G). So, I did a ln transformation of the dose variable, and then proceeded with the logistic regression.

Some important output from the analysis:

Beta_hat = 3.3364
95% Likelihood Ratio Confidence Interval for Beta = (2.6478, 4.0989)


This is pretty much a multi-step type question... I've answered questions a) through f), but I am getting really confused on questions g) and h)

Here are the questions, verbatim.

g) Given an approximate 95% Likelihood Ratio Confidence Interval for B. Translate this interval into an interval for the effect on the odds of death of increasing the dose by 50% (ie., multiplying the dose by 1.5) and interpret. Hint: First translate the multiplying dose factor to the natural log scale.

For this question, I've been going with this interpretation.

e^Beta_hat = e^3.3364 = 28.12. Thus, for a one-unit increase in the log dose, there is a 28.12 multiplicative effect on the odds in favor of insect death. I'm just having trouble proceeding with the next parts...logarithms and all.

I need help converting the interval so I can say something like this. For a 50% increase in Dose (Not Log dose), there is a ___ multiplicative effect on the odds in favor of insect death, CI (___, ____)

h) Setup an approximate 95% CI for the rate of change of the chance of death per unit increase in log concentration at the median effective level.

Any help would be great. Like I said, its just these last two questions that are really confusing me.

Cheers