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Logistic Regression

Sigmoid Function

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!

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`

.

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`

.

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`

.