data(aflatoxin)

use R

Problem 2. (on page 80 of the textbook) Aflatoxin Bl was fed to lab animals at various doses and the number responding with liver cancer recorded. The data may be found in the dataset aflatoxin. (a) Plot the proportion of animals with liver cancer against the dose. (b) Fit a logistic regression for the number of animals with liver cancer as a function ofthe dose. Assess the statistical significance of the dose with two different tests. Which test is preferable? (c) For the fitted model, compute the predicted probability of liver cancer over the range of the data. Show the predicted curve on top of the data shown in (a). (d) Change to a probit link. Compute the predicted probability under this model and add the curve to the existing plot. (e) Compute the predicted probability of liver cancer for a dose of 25 ppb on the link scale. Compute a 95% confidence interval. Transform onto the probability scale. (f) Compute the predicted probability directly on the probability scale and report the standard error. Use this standard error to construct a 95% confidence interval for the probability. Which of the two methods of computing the CI as seen in this and the previous question is preferable? (g) Compute the effective dose at 1%, 10% and at 50% levels with associated standard error. Remark on any incongruity in your calculated effective doses