10.4 Table 10.9 shows the free-throw shooting, by game, of Shaq O’Neal of the Los Angeles Lakers during the 2000 NBA (basketball) playoffs. In game i, let yi = number made out of Ti attempts.

a. Fit the model, logit(πi ) = ui + α, where {ui } are independent N(0, σ), and given {ui }, {yi } are independent binomial variates for {Ti } trials with success probabilities {πi }. Report ˆα and ˆσ .

b. Use ˆα to summarize O’Neal’s free-throw shooting in an average game

(for which ui = 0).

c. Use ˆα and ˆσ to estimate how O’Neal’s free-throw shooting varies among games.