3. The frequencies of disease and exposure status are arranged in the following table. Exposure Disease...

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3. The frequencies of disease and exposure status are arranged in the following table. Exposure Disease status status D D noo no1 no- 110 n11 n1- 12.0 12.1 n.. Ix, be Let us assume that the counts follow a Binomial distribution with p = P(D), and x = the indicator of exposure. Consider a linear logistic regression model log{p/(1-p)} = a+x, and express your answers to the following questions in terms of the counts nij. (a) Calculate the MLE of and B. (b) Treating the counts as two Binomial observations, one with x=0 and the other with x=1, calculate the deviance of the fit. (c) Treating the data as n.. Bernoulli observations, no. of which have x = 0, and the remain- ing n. have x = 1, calculate the deviance of the fit. (d) Calculate the information matrix I(, B). 3. The frequencies of disease and exposure status are arranged in the following table. Exposure Disease status status D D noo no1 no- 110 n11 n1- 12.0 12.1 n.. Ix, be Let us assume that the counts follow a Binomial distribution with p = P(D), and x = the indicator of exposure. Consider a linear logistic regression model log{p/(1-p)} = a+x, and express your answers to the following questions in terms of the counts nij. (a) Calculate the MLE of and B. (b) Treating the counts as two Binomial observations, one with x=0 and the other with x=1, calculate the deviance of the fit. (c) Treating the data as n.. Bernoulli observations, no. of which have x = 0, and the remain- ing n. have x = 1, calculate the deviance of the fit. (d) Calculate the information matrix I(, B).