Logistic Regression

A logistic regression is a regression model where the target Y variable (also called the dependent variable) is categorical. Wikipedia: Logistic regression

Key Statements
# Inputs: x_train, y_train, x_test, y_test.

# Fit the model.
from sklearn.linear_model import LogisticRegression
model = LogisticRegression().fit(x_train, y_train)

# Get predictions.
y_predict_proba = model.predict_proba(x_test)
y_predict = [int(proba[1] > 0.5) for proba in y_predict_proba]

# Get the confusion matrix results.
from sklearn.metrics import confusion_matrix
matrix = confusion_matrix(y_test, y_predict)
Working End-to-End Example
# Step 1: Import the libraries.
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import confusion_matrix
from sklearn.model_selection import train_test_split


# Step 2: Set up the constants.
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

# The target feature is whether or not the employee left.
TARGET_FEATURE = 'left'  # Valid data values are 0 or 1.

# We'll set aside 20% of the data to test the model.
TEST_SET_SIZE = 0.2

# We need to know which features are categorical.
CATEGORICAL_FEATURES = ['sales', 'salary']


# Step 3: Load in the raw data.
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

# This assumes the data is in the same directory as this script.
# Here we load the data into a pandas DataFrame.
raw_data = pd.read_csv('HR_comma_sep.csv')

# It's helpful to take a quick look at the data.
print('Sample of loaded data:')
print(raw_data.sample(5))
print('')
print('Count per value (0 or 1) of the target feature:')
print(raw_data[TARGET_FEATURE].value_counts())
print('')


# Step 4: Set up the data.
# ~~~~~~~~~~~~~~~~~~~~~~~~

# Separate the X and Y values.
y_data = raw_data[TARGET_FEATURE]

# Using drop() doesn't change raw_data, only the return value.
# The axis=1 keyword tells pandas to drop a column (not a row).
x_data = raw_data.drop(TARGET_FEATURE, axis=1)

# To include an intercept, add a new column with a constant.
x_data['intercept'] = 1.0

# Turn categorical variables into dummy columns (0 or 1 values).
# Do this to avoid assuming a meaningful order of categories.
# Use drop_first to avoid multicollinearity among features.
x_data = pd.get_dummies(
    x_data,
    columns=CATEGORICAL_FEATURES,
    drop_first=True
)

# It's helpful to double check that the final data looks good.
print('Sample of data to use:')
print(x_data.sample(5))
print('')

# Split the data into training and test sets.
x_train, x_test, y_train, y_test = train_test_split(
    x_data,
    y_data,
    test_size=TEST_SET_SIZE
)


# Step 5: Fit the model.
# ~~~~~~~~~~~~~~~~~~~~~~

model = LogisticRegression().fit(x_train, y_train)

# Yes, that's it!


# Step 6: Get the results.
# ~~~~~~~~~~~~~~~~~~~~~~~~

# Get prediction probabilities for the test set.
y_predict_proba = model.predict_proba(x_test)

# The value y_predict_proba[i, j] is the model's prediction for
# prob(y[i] = j), where j = 0 or 1; y[i] is the ith target value.
# Convert to 0 or 1: y_predict[i] = 1 when prob(y[i] = 1) > 0.5.
cutoff = 0.5
y_predict = [int(proba[1] > cutoff) for proba in y_predict_proba]

# Get the confusion matrix and calculate the results.
#   M[i][j] = #cases with known value i and predicted value j.
M = confusion_matrix(y_test, y_predict)
n_samples = len(y_test)
print('Accuracy:  %.2f' % ((M[0][0] + M[1][1]) / n_samples))
print('Precision: %.2f' % (M[1][1] / (M[0][1] + M[1][1])))
print('Recall:    %.2f' % (M[1][1] / (M[1][0] + M[1][1])))

Notes

Beware of multicollinearity, which can cause issues.

Variables can have any distribution; they don't need to be normally distributed.