Chapter 5.1, Problem 4E

Special Rounding Instructions When you perform logistic regression, round the $r$ value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless otherwise indicated.

Baseball Hall of Fame The number of lifetime home runs $H$ for a Major League Baseball player is related to the probability $P$ (as a percent) that he will be inducted into the Hall of Fame. A proposed relationship is

$P=\frac{100}{1+383.75e^{-0.0143H}}$.

a. Plot the graph of $P$ versus $H$. Include values on $H\text{-axis}$ up to $700$ home runs.

b. Mickey Mantle had $536$ career home runs. According to this model, what were his chances of getting into the Hall of Fame?(Mickey Mantle is in the Hall of Fame.)

c. A Major League Baseball player hopes to make the Hall of Fame. Does a home run today have a greater effect on his chances if he currently has $400$ or $500$ career home runs.