Question

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.

Answer 1

Answer:

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)