📈 MemoLearning Linear Regression

Master linear regression modeling for prediction and relationship analysis

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Linear Regression Curriculum

12
Core Units
~75
Regression Concepts
15+
Evaluation Metrics
25+
Practical Examples
1

Introduction to Regression

Understand the fundamental concepts of regression analysis and its applications in data science.

  • What is regression analysis
  • Types of regression problems
  • Dependent vs independent variables
  • Linear vs non-linear relationships
  • Prediction vs explanation
  • Regression vs classification
  • Applications in business
  • Historical context
2

Simple Linear Regression

Master the basics of simple linear regression with one predictor variable.

  • Linear relationship concept
  • Regression line equation
  • Slope and intercept interpretation
  • Least squares method
  • Residuals and errors
  • Coefficient estimation
  • Scatter plots and visualization
  • Hands-on implementation
3

Multiple Linear Regression

Extend to multiple predictor variables and understand multivariate relationships.

  • Multiple regression equation
  • Partial regression coefficients
  • Matrix formulation
  • Adding variables to models
  • Interpretation with multiple predictors
  • Interaction effects
  • Model complexity considerations
  • Real-world examples
4

Assumptions and Diagnostics

Learn the key assumptions of linear regression and how to validate them.

  • Linearity assumption
  • Independence of observations
  • Homoscedasticity
  • Normality of residuals
  • No multicollinearity
  • Diagnostic plots
  • Assumption testing
  • Violation consequences
5

Model Evaluation Metrics

Understand various metrics to assess regression model performance and goodness of fit.

  • R-squared and adjusted R-squared
  • Mean squared error (MSE)
  • Root mean squared error (RMSE)
  • Mean absolute error (MAE)
  • Mean absolute percentage error
  • Residual analysis
  • Cross-validation metrics
  • Model comparison techniques
6

Feature Selection

Learn methods to select the most relevant features for regression models.

  • Forward selection
  • Backward elimination
  • Stepwise selection
  • Best subset selection
  • Information criteria (AIC, BIC)
  • Cross-validation approach
  • Regularization preview
  • Domain knowledge integration
7

Regularization Techniques

Prevent overfitting and improve generalization using Ridge, Lasso, and Elastic Net.

  • Overfitting in regression
  • Ridge regression (L2)
  • Lasso regression (L1)
  • Elastic Net
  • Hyperparameter tuning
  • Cross-validation for λ selection
  • Feature selection with Lasso
  • Comparison of methods
8

Polynomial Regression

Model non-linear relationships using polynomial features and transformations.

  • Non-linear relationships
  • Polynomial features
  • Degree selection
  • Overfitting with polynomials
  • Feature transformations
  • Interaction terms
  • Visualization techniques
  • Practical considerations
9

Logistic Regression

Extend linear regression concepts to classification problems using logistic regression.

  • From linear to logistic
  • Logit function and odds
  • Maximum likelihood estimation
  • Sigmoid function
  • Binary classification
  • Multinomial logistic regression
  • Model interpretation
  • Performance evaluation
10

Model Interpretation

Learn to interpret regression coefficients and communicate model insights effectively.

  • Coefficient interpretation
  • Statistical significance
  • Confidence intervals
  • Effect size and practical significance
  • Partial effects
  • Standardized coefficients
  • Feature importance
  • Business interpretation
11

Advanced Topics

Explore advanced regression topics including time series and robust regression methods.

  • Time series regression
  • Robust regression
  • Weighted least squares
  • Bayesian linear regression
  • Mixed effects models
  • Non-parametric regression
  • Survival analysis regression
  • Advanced diagnostics
12

Practical Implementation

Apply regression techniques to real-world datasets and build end-to-end projects.

  • Data preprocessing for regression
  • Scikit-learn implementation
  • Model pipeline creation
  • Cross-validation strategies
  • Hyperparameter optimization
  • Model deployment considerations
  • Case studies
  • Best practices and pitfalls

Unit 1: Introduction to Regression

Understand the fundamental concepts of regression analysis and its applications in data science.

What is Regression Analysis

Learn regression as a statistical method for modeling relationships between variables and making predictions.

Modeling Prediction Relationships
Regression analysis examines the relationship between a dependent variable and one or more independent variables to understand patterns and make predictions.

Types of Regression Problems

Understand different types of regression based on the nature of variables and relationships.

# Types of regression problems:
# 1. Simple vs Multiple regression
# 2. Linear vs Non-linear regression
# 3. Continuous vs Discrete outcomes
# 4. Parametric vs Non-parametric

Dependent vs Independent Variables

Distinguish between response variables (what we predict) and predictor variables (what we use to predict).

Y = f(X₁, X₂, ..., Xₚ) + ε
Y: Dependent variable (response)
X: Independent variables (predictors)
# Example: House price prediction
# Dependent: house_price (what we predict)
# Independent: size, location, bedrooms (predictors)
y = df['house_price']
X = df[['size', 'bedrooms', 'location']]

Linear vs Non-linear Relationships

Identify when relationships between variables are linear versus when they require non-linear modeling.

Linear: Change in X produces constant change in Y
Non-linear: Change in X produces varying change in Y
import matplotlib.pyplot as plt
# Visualize relationship
plt.scatter(X, y)
plt.xlabel('Independent Variable')
plt.ylabel('Dependent Variable')
# Look for linear pattern

Prediction vs Explanation

Understand the difference between using regression for prediction versus explanation of relationships.

Prediction Focus: "What will Y be for new X values?"
Explanation Focus: "How does X affect Y?"
# Prediction focus
predicted_price = model.predict([[2000, 3, 'downtown']])

# Explanation focus
print(f"Each additional bedroom increases price by ${model.coef_[1]:.2f}")

Regression vs Classification

Distinguish between regression (continuous outcomes) and classification (categorical outcomes) problems.

Continuous Categorical
# Regression: Predicting house price ($100K, $200K, $350K)
# Classification: Predicting house type (small, medium, large)

# Regression target
y_regression = [100000, 200000, 350000]
# Classification target
y_classification = ['small', 'medium', 'large']

Applications in Business

Explore common business applications where regression analysis provides valuable insights.

• Sales forecasting
• Price optimization
• Marketing effectiveness
• Risk assessment
• Customer lifetime value
# Business example: Sales prediction
# Predict monthly sales based on:
# - Advertising spend
# - Seasonality
# - Economic indicators
# - Competitor actions

Historical Context

Learn about the development of regression analysis and its evolution in data science.

Regression was first developed by Francis Galton in the 19th century, originally to study the relationship between parents' and children's heights - hence "regression to the mean."

Unit 2: Simple Linear Regression

Master the basics of simple linear regression with one predictor variable.

Linear Relationship Concept

Understand what constitutes a linear relationship and how to identify it in data.

Linear Relationship: Y = β₀ + β₁X + ε
Constant rate of change between X and Y
import numpy as np
import matplotlib.pyplot as plt
# Perfect linear relationship
X = np.array([1, 2, 3, 4, 5])
y = 2 * X + 1 # slope=2, intercept=1
plt.plot(X, y)

Regression Line Equation

Learn the mathematical form of the regression line and what each component represents.

ŷ = β₀ + β₁x
ŷ: predicted value
β₀: y-intercept
β₁: slope coefficient
from sklearn.linear_model import LinearRegression
# Fit simple linear regression
model = LinearRegression()
model.fit(X.reshape(-1, 1), y)
print(f"Intercept: {model.intercept_}")
print(f"Slope: {model.coef_[0]}")