Thinking about log odds can be confusing, though. This also tells us that for every 1 unit increase in X, the log odds increases by 1.2 (a 2 unit increase in X results in an increase to the log odds of 2.4, etc.). This means that when X = 0, the log odds equals -5.5. Let’s say our simple logistic regression model was Ln(odds) = -5.5 + 1.2*X.
Although you’ll often see these coefficients referred to as intercept and slope, it’s important to remember that they don’t provide a graphical relationship between X and P(Y=1) in the way that their counterparts do for X and Y in simple linear regression. For simple logistic regression (like simple linear regression), there are two coefficients: an “intercept” (β0) and a “slope” (β1). Now that we know how logistic regression uses log odds to relate probabilities to the coefficients, we can think about what these coefficients are actually telling us.
