# Logistic Regression

Despite having “regression” in its name, a logistic regression is actually a widely used binary classifier (i.e. the target vector can only take two values). In a logistic regression, a linear model (e.g. $\beta_{0}+\beta_{1}x$) is included in a logistic (also called sigmoid) function, ${\frac{1}{1+e^{-z}}}$, such that:

$$P(y_i=1 \mid X)={\frac{1}{1+e^{-(\beta_{0}+\beta_{1}x)}}}$$

where $P(y_i=1 \mid X)$ is the probability of the $i$th observation’s target value, $y_i$, being class 1, $X$ is the training data, $\beta_0$ and $\beta_1$ are the parameters to be learned, and $e$ is Euler’s number.

## Preliminaries

# Load libraries
from sklearn.linear_model import LogisticRegression
from sklearn import datasets
from sklearn.preprocessing import StandardScaler

# Load data with only two classes
X = iris.data[:100,:]
y = iris.target[:100]

## Standardize Features

# Standarize features
scaler = StandardScaler()
X_std = scaler.fit_transform(X)

## Create Logistic Regression

# Create logistic regression object
clf = LogisticRegression(random_state=0)

## Train Logistic Regression

# Train model
model = clf.fit(X_std, y)

## Create Previously Unseen Observation

# Create new observation
new_observation = [[.5, .5, .5, .5]]

## Predict Class Of Observation

# Predict class
model.predict(new_observation)
array([1])


## View Predicted Probabilities

# View predicted probabilities
model.predict_proba(new_observation)
array([[ 0.18823041,  0.81176959]])