# stat 557

## Homework II

## Due Date: Sep 27

### Negative Binomial

A random variable X that follows a negative binomial distribution with parameter r can be considered to count the number of attempts x of independent trials with success probability p before succeeding for the rth time. (see here for a definition, or 4.12 on p.131 in Agresti)

Show that for fixed dispersion parameter phi the negative binomial distribution is a member of the exponential family.
### Still Happy!?

Based on the GSS's survey on people's happiness, consider the model from the lab session. Here, we restricted the analysis to only consider extreme ends of the scale: very happy and not very happy individuals.
Using this subset, compare models of happiness versus highest degree, where highest degree is coded as a factor variable first, then using it as a linear co-variate with score values c(1,2,3,4,5), c(2,4,6,8,10) and c(1,2,4,6,7).

Compare each of the score models with the first model.
How do overall fit, coefficients and predictions change?

Show (first in the model, and then sketch out theoretically) that predictions are only affected by changes to the ratio between factors.
### Kobe Bryant

Based on nba.com, Kobe Bryant's game by game performance for the 2011 season can be found here.
The variables X3PM and X3PMA report the number of successful 3 point throws and the number of attempts, respectively.
- Investigate claims, that Bryant's 3-point performance over the 2011 season got worse. Plot the percentage of successful 3-point shots over the season (game). Use a binomial generalized linear model. Report and interpret your findings.
Investigate whether there is any indication of over- or underdispersion?
- Discuss whether any perceived worse 3-point performance could be due to number of attempts. Plot the number of 3-point attempts over the season. Now fit a Poisson generalized model, and, again, report and interpret your findings.
- Extra point: is there a home court effect? - Show all your work and conclusions.