Using a little bit of algebra, prove that (4.2) is equivalent to (4.3). In other words, the logistic function representation and logit representation for the logistic regression model are equivalent.

The logistic function representation and logic representation for the logistic regression model are equivalent.

Step-by-step explanation:

Y (X) = e ^ (B 0 + B 1) / (1+e^ (B 0 + B1x)) ... 4.2

P (x) / (1-P (x)) = e^ (B 0 + B 1x) ... 4.3

Let

Y (X) = e^ (B 0 + B1x)

1/p (X) = 1+e^ (B 0 + B1x)

P (x) = Y (x) / (1+Y (x))

P (x) (1+Y (x)) = Y (x)

Expanding;

P (x) + P (x) Y (x) = Y (x)

P (x) = Y (x) - P (x) Y (x)

P (x) = Y (x) (1-P (x))

P (x) / (1-P (x)) = Y (x)

P (x) / (1-P (x)) = e^ (B 0 + B 1x)