Therefore, e β0 is the Odds when X is zero. When X equals 0, the second term equals 1.0. Using some rules for exponents, we can obtain: So using the math described above, we can re-write the simple logistic regression model to tell us about the odds (or even about probability). 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. β1: how much the log odds change with an increase (or decrease) in X by 1.0.β0: the log odds when the X variable is 0.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.
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