Logistic Regression

Understanding the Sigmoid Function

$$ \sigma(z) = \frac{1}{1 + e^{-z}} $$

$$ z = \beta_0 + \beta_1 x $$

School

β₀ (intercept) 0.0

β₁ (slope) 1.0

x (input) 0.0

Tip: Use ◀ ▶ arrows above to see equivalent notations for z. The formula stays the same, just different letters!

                P(y=1) = 50.0%
            

Linear lines ($z$) go from $-\infty$ to $+\infty$. This is bad for probabilities. The Sigmoid function "squashes" any number into [0, 1].

When $z = 0$, probability is exactly 50%.
$z > 0$ → Class 1 | $z < 0$ → Class 0