Key Concepts Study Tool: Chapter 17

1. Logistic Regression

An alternative to OLS regression when the outcome variable, Y (our dependent variable) is not continuous.
Predicts the log odds that an observation will have an indicator equal to one, where the odds of an event is the ratio of the probability that an event occurs to the probability that it will not (i.e the odds ratio)
This is read as the odds of Y being equal 1, are equal to the probability of a positive occurrence over the probability of a negative occurrence.

2. Logistic Regression: The Formula

Instead of modelling the odds, we model the natural logarithm of the odds:
The dependent variable is referred to as the logit.
Logistic coefficients reflect the effect of a 1-increment change in the DV on the log odds of the DV being equal to 1 (or the log odds of the DV occurring).
Log odds are completely symmetrical and lie in the range of –∞ to +∞.

3. Modelling Logistic Regression

Log odds remove the theoretical upper and lower bounds on the DV in logistic regression. The equation:
LogOdds(Y = 1) = a + b₁x_li+ b₂x_2i+ ... b_nx_ni+ e_i
To get a better sense of the magnitude of difference, and to make interpretation of the logistic coefficients easier, we can exponentiate the results: Oddsratio_x1=e^b1
Exponentiation is the inverse function of the logarithm so the log odds will be changed into odds.