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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 [0,1].

$h(z)=\frac{1}{1+e^{-z}}$
• e^(-z) is the exponential function, which can be written in numpy as np.exp(-z)

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!

### Instructions

1.

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 z.

2.

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 z, return 1/denominator.

3.

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 probabilities.