Kupper and Haseman (1978) describe vaguely an experiment in which pregnant female mice were assigned to one of two groups, labeled "treatment" and "control." The data are available in the mice data frame of the aod package. From each female the number of pups born in the litter (n) and the count of those that were affected in some way (y) were recorded.

(a) Fit a Logistic regression model to these data. Test the significance of the treatment effect and find a confidence interval for the odds ratio for the effect of "treatment" relative to "control."

(b) Note that the number of explanatory variable levels is fixed, so it would not increase if the sample size were to grow. This means that we can use the residual deviance to test the fit of the model formally. Perform this test. State the hypotheses, the test statistic, the p-value, and the conclusions.

(c) Fit a quasi-binomial regression model and repeat the analysis from part (a). Are the results substantially different?

(d) Use a beta-binomial model to repeat the analysis from part (a). This can be done using the betabin() function of the package aod. Are the results substantially different?