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_iattempts is a bin(n_i, Ï€_i) variate and {y_i} are independent.

a. Fit the model, logit(π_i) = α. Find and interpret π̂_i. Does the model appear to fit adequately?

b. Fit the model, logit(Ï€_i) = α + u_i, where {u_i} are independent N(0, σ²). Use α̂ and σ̂ to summarize O€™ Neal€™s free-throw shooting.

c. Explain how the model in part (a) is a special case of that in part (b). Is there evidence that the one in part (b) fits better?

Table 4.8:

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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