How did our Logistic Regression model create the S-shaped curve we previously saw? The answer is the Sigmoid Function.
The Sigmoid Function is a special case of the more general Logistic Function, where Logistic Regression gets its name. Why is the Sigmoid Function so important? By plugging the log-odds into the Sigmoid Function, defined below, we map the log-odds
z to the range
e^(-z)is the exponential function, which can be written in
This enables our Logistic Regression model to output the probability of a sample belonging to the positive class, or in our case, a student passing the final exam!
Let’s create a Sigmoid Function of our own! Define a function called
sigmoid() that takes
z as a parameter. For now, have it return
Inside the function and above the return statement, create a variable
denominator and set it equal to 1 plus the exponential of
-z. Instead of returning
All done! Now test out your function by plugging in the
calculated_log_odds we found in the previous exercise and saving the result to
probabilities. Then, print