The number of hospital admissions for respiratory conditions in a big city was recorded over 150 days. The level of the concentration of a certain pollutant was also recorded (‘low’, ‘medium’, ‘high’), together with the mean temperature (in degrees Celsius) on the day. Part of the data is shown below. A generalised linear model is to be fitted to investigate the dependence of the number of hospital admissions on mean temperature and pollutant concentration. (i) Write down a suitable model for the number of hospital admissions. I didn't find any clue in the title to specify the use of Poisson, but in the answer tell us using Poisson. Why? I guess it might be because Poisson can be replaced by other 4 types and the link function will change accordingly, is that so?
you are modelling the number of hospital admissions, we want a discrete distribution, so this can be modelled by a Poisson distribution as it is a rate, not Binomial
