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Overview

Linear regression is a supervised machine learning algorithm used to model the relationship between a dependent variable and one or more independent variables. In this ecommerce analysis, we use linear regression to predict the Yearly Amount Spent by customers based on their engagement metrics.

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Why Linear Regression?

Linear regression was chosen for this problem for several key reasons:
  • Interpretability: The coefficients provide clear insights into how each feature impacts customer spending
  • Continuous Target Variable: Yearly spending is a continuous numerical value, making it ideal for regression
  • Linear Relationships: Initial data exploration indicated approximately linear relationships between features and the target
  • Baseline Performance: Linear regression serves as an excellent baseline model before exploring more complex algorithms
  • Business Insights: The model coefficients directly inform business decisions about resource allocation

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Model Assumptions

Linear regression operates under several key assumptions:
  1. Linearity: The relationship between independent and dependent variables is linear
  2. Independence: Observations are independent of each other
  3. Homoscedasticity: Constant variance of residuals across all levels of independent variables
  4. Normality: Residuals are normally distributed
  5. No Multicollinearity: Independent variables are not highly correlated with each other
While these assumptions are important for optimal model performance, linear regression can still provide valuable insights even when some assumptions are partially violated.

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Features Used

The model uses four key features to predict yearly customer spending:
FeatureDescriptionUnit
Avg. Session LengthAverage duration of in-store style and clothing advice sessionsMinutes
Time on AppTime spent on the mobile applicationMinutes
Time on WebsiteTime spent on the websiteMinutes
Length of MembershipHow long the customer has been a memberYears

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Target Variable

Yearly Amount Spent: The total amount spent by the customer annually (in dollars)

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Mathematical Formulation

The linear regression model predicts the target variable using the following equation: 
Yearly Amount Spent = β₀ + β₁(Avg. Session Length) + β₂(Time on App) + β₃(Time on Website) + β₄(Length of Membership)
Where:
  • β₀ (intercept): The baseline value when all features are zero
  • β₁, β₂, β₃, β₄ (coefficients): The weight assigned to each feature, indicating its impact on the target variable

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Interpretation

Each coefficient represents the change in yearly spending (in dollars) for a one-unit increase in the corresponding feature, holding all other features constant.
For example, if β₂ (Time on App coefficient) is 38.81, this means that for every additional minute spent on the mobile app, the model predicts an increase of approximately $38.81 in yearly spending.

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Model Implementation

The model is implemented using scikit-learn’s LinearRegression class, which uses the Ordinary Least Squares (OLS) method to find the optimal coefficients that minimize the sum of squared residuals. 
from sklearn.linear_model import LinearRegression

# Initialize the model
lr_model = LinearRegression()
This implementation:
  • Automatically calculates optimal coefficients using matrix operations
  • Handles multiple features efficiently
  • Provides methods for fitting and prediction
  • Includes no regularization (pure OLS)

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