Logistic Regression

Logistic Regression will model the probability that a response belongs to 1 of 2 categories.

We do not use linear regression since we wish to have values in the range $[0,1]$.

Logistic Regression will model the probability of a response belonging to a certain category.

We use the following function

$$p(X)=\frac{e^{{\beta }_0+{\beta }_{1}X}}{1+e^{{\beta }_0+{\beta }_{1}X}}$$

$p$ has a domain $\in [0,1]$