Module 4: Linear Correlation and Regression
Introduction
In this module, we'll transition from hypothesis testing to understanding and quantifying relationships between variables. Linear correlation and regression are foundational statistical techniques used to measure the strength of relationships between variables and to build predictive models.
These methods allow us to answer questions like: How strongly are two variables related? Can we use one variable to predict another? Is there a meaningful linear relationship between variables? These are crucial skills for data scientists, as they form the basis for more advanced predictive modeling techniques.
Learning Objectives
By the end of this module, you should be able to:
- Calculate and interpret correlation coefficients
- Determine the statistical significance of correlations
- Construct simple linear regression models
- Interpret regression coefficients and understand their meaning
- Assess the quality of regression models using R-squared
- Make predictions using regression equations
- Understand the assumptions and limitations of linear regression
- Use Python to implement correlation and regression analyses
Guided Project
Project Resources
Open DS_124_Linear_Correlation_and_Regression.ipynb in the GitHub repository below to follow along with the guided project:
GitHub: Linear Correlation and RegressionKey Concepts
- Pearson's correlation coefficient and its interpretation
- Correlation vs. causation
- Simple linear regression model equation: y = mx + b
- Ordinary Least Squares (OLS) estimation
- Coefficient of determination (R-squared)
- Residuals and prediction errors
- Statistical significance of regression coefficients
- Assumptions of linear regression
Module Project
Project Tasks
In this module's project, you will be asked to:
- Calculate correlation coefficients between variables
- Interpret the strength and direction of correlations
- Create scatter plots to visualize relationships
- Build simple linear regression models
- Interpret regression coefficients and intercepts
- Evaluate model fit using R-squared
- Make predictions using regression equations
- Analyze residuals to assess model quality
Complete all tasks in the Jupyter notebook provided in the GitHub repository.