Table 8.3 shows the three-point shooting, by game, of Ray Allen of the Boston Celtics during the 2010 NBA (basketball) playoffs (e.g., he made 0 of 4 shots in game 1). Commentators remarked that his shooting varied dramatically from game to game. In game i, suppose that niyi = number of three-point shots made out of ni attempts is a bin(ni, ????i) variate and the {yi} are independent.

Table 8.3 Data for Exercise 8.17 on Three-Point Shooting in Basketball Game yi Game yi Game yi Game yi Game yi 1 0/4 6 2/7 11 0/5 16 1/3 21 0/4 2 7/9 7 3/7 12 2/5 17 3/7 22 0/4 3 4/11 8 0/1 13 0/5 18 0/2 23 2/5 4 3/6 9 1/8 14 2/4 19 8/11 24 2/7 5 5/6 10 6/9 15 5/7 20 0/8 Source: http://boston.stats.com/nba. Data at file Basketball.dat at text website.

a. Fit the model, ????i = ????0. Find and interpret ????̂

0 and its standard error.

b. Describe a factor that could cause overdispersion. Adjust the standard error for overdispersion. Using the original SE and its correction, find and compare 95% confidence intervals for ????0. Interpret.