Table 4.8 shows the free-throw shooting, by game, of Shaq O€™NeaI of the Los Angeles Lakers during the 2000 NBA (basketball) playoffs. Commentators remarked that his shooting varied dramatically from game to game. In game i, suppose that Y_i= number of free throws made out of n_iattempts is a bin(n_i, Ï€_i) variate and the {Y_i} are independent.

a. Fit the model, Ï€_i = α, and find and interpret α̂ and its standard error. Does the model appear to fit adequately? 

b. Adjust the standard error for overdispersion. Using the original SE and its correction, find and compare 95% confidence intervals for α. Interpret.

Table 4.8:

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Number Number of Number Number of Number Number of Game Made Attempts Game Made Attempts Game Made Attempts 4 12 4 27 17 12 4 17 18 19 12 11 14 12 10 11 12 13 14 15 16 2 3 4 5 13 5 39 13 17 5 5 18 3 10 20 21 22 23 10 14 15 12 10 12 3 3 +nn n2709