Chapter 4, Problem 1E

Explanation of Solution

Logistic function

• The logistic function representation and logit representation for the logistic regression model are equivalent.
• Here the equation is $\text{p(X)=}\frac{{\text{e}}^{{\text{β}}_{\text{0}}{\text{+β}}_{\text{1}}\text{X}}}{{\text{1+e}}^{{\text{β}}_{\text{0}}{\text{+β}}_{\text{1}}\text{X}}}\iff {\text{e}}^{{\text{β}}_{\text{0}}{\text{+β}}_{\text{1}}\text{X}}\text{(1-p(X)) = p(X),}$
• It is equivalent to  ${\text{p(X)/1-p(X)=e}}^{\text{β}}{{}_{\text{0}}}^{\text{+ β}}{{}_{\text{1}}}^{\text{X}}$