In Problem 12.2 about Shaq O€™Neal€™s free-throw shooting, the simple binomial model, Ï€_i= α, has lack of fit. Fit the beta-binomial model, or use the quasi-likelihood approach with that variance structure. Use the fit to summarize his free-throw shooting, by giving an estimated mean and standard deviation for Ï€_i.

Problem 12.2:

Refer to Table 4.8 on the free-throw shooting of Shaq O€™Neal. In game i, suppose that y_i = number made out of n_i attempts is a bin(n_i, Ï€_i) variate and {y_i} are independent.

Table 4.8:

Number Number of Game Made Attempts Game Made 5 11 Number Number of Number Number of Attempts Attempts Game Made 12 4 27 17 18 19 4 5 5 5 2 1 4 12 10 11 3 4 13 5 39 18 14 12 3 12 13 14 20 13 17 12 21 22 10 17 10 14 15 6. 23 3 12 10 12 15 16 3