For games in baseball€™s National League during nine decades, Table 4.6 shows the percentage of times that the starting pitcher pitched a complete game.

a. Treating the number of games as the same in each decade, the ML fit of the linear probability model is π̂ = 0.7578 €“ 0.0694x, where x = decade (x = 1,2,.. . .9). Interpret 0.7578 and €“ 0.0694.

b. Substituting x = 10, 11, 12, predict the percentages of complete games for the next three decades. Are these predictions plausible? Why?

c. The ML fit with logistic regression is π̂ = exp(l.148 €“ 0.315x)/[1+ exp(l.148 €“ 0.315x)]. Obtain π̂_i for x = 10, 11, 12. Are these more plausible?

Table 4.6:

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Percent Complete Percent Percent Complete 27.2 22.5 13.3 Decade Decade Decade 1930–1939 1940-1949 1950–1959 Complete 44.3 41.6 32.8 1900–1909 1910–1919 1920–1929 72.7 63.4 1960–1969 1970-1979 1980–1989 50.0