A study analyzed the probability of Major League Baseball (MLB)players to "survive"
for another season, or, in other words, to play one more season.The researchers had a
sample of 4,728 hitters and 3,803 pitchers for the years 1901-1999.All explanatory
variables are standardized.The probit estimation yielded the results as shown in the
table:

\begin{array} { | c | c | c | } \hline \text { Regression } & \text { (1) Hitters } & \text { (2) Pitchers } \\\hline \text { Regression model } & \text { probit } & \text { probit } \\\hline \text { constant } & 2.010 & 1.625 \\& ( 0.030 ) & ( 0.031 ) \\\hline \text { number of seasons } & - 0.058 & - 0.031 \\\text { played } & ( 0.004 ) & ( 0.005 ) \\\hline \text { performance } & 0.794 & 0.677 \\& ( 0.025 ) & ( 0.026 ) \\\hline \text { average performance } & 0.022 & 0.100 \\& ( 0.033 ) & ( 0.036 ) \\\hline\end{array}

where the limited dependent variable takes on a value of one if the player had one more
season (a minimum of 50 at bats or 25 innings pitched), number of seasons played is
measured in years, performance is the batting average for hitters and the earned run
average for pitchers, and average performance refers to performance over the career.
16
(a)Interpret the two probit equations and calculate survival probabilities for hitters and
pitchers at the sample mean.Why are these so high?

To Measure the Fit of the Probit Model, You Should R2R ^ { 2 }R2

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To Measure the Fit of the Probit Model, You Should $R ^ { 2 }$

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