Statistics 4F03/6F03 - Test #1

2006-10-12 18:00-20:00


This test is to be written in the BSB Student Technology Centre. The duration of the test is 2 hours.
Any aids and resources are permitted. You may consult any web pages but you may not use e-mail or communicate with anyone other than the instructor.

Part A.

Question 1.

Consider linear Poisson regression through the origin, mu = beta*x. Find the log-likelihood, score and information for beta. Pick some x-values and generate data from this model. Plot your data. Use scoring to fit the data and find 95% confidence intervals for beta by the likelihood-ratio, score and Wald methods. Compare your results with

summary(glm(y ~ x - 1, family = poisson(link = identity)))

Question 2.

Consider log-linear Poisson regression through the origin, log(mu) = beta*x. Find the log-likelihood, score and information for beta. Pick some x-values and generate data from this model. Plot your data. Use scoring to fit the data and find 95% confidence intervals for beta by the likelihood-ratio, score and Wald methods. Compare your results with

summary(glm(y ~ x - 1, family = poisson(link = log)))

Part B.

The numbered problems are from Agresti, A. (2002), Categorical Data Analysis, Wiley.

Chapter 2

2.3, 2.8


Statistics 4F03/6F03