Module 11: Simple Linear Regression
Analyzing relationships between two quantitative variables using correlation and regression
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Module Overview
In this module, you'll learn how to analyze relationships between two quantitative variables. We'll explore correlation (measuring the strength of linear relationships), simple linear regression (predicting one variable from another), hypothesis testing for correlation and slope, and constructing confidence and prediction intervals. This is one of the most practical and widely-used statistical tools!
Learning Objectives
By the end of this module, you will be able to:
- Create and interpret scatter plots to visualize bivariate relationships
- Calculate and interpret the correlation coefficient (r)
- Understand the difference between correlation and causation
- Find the equation of the least-squares regression line
- Calculate and interpret the coefficient of determination (r²)
- Make predictions using the regression equation
- Calculate and interpret residuals
- Perform hypothesis tests for correlation and slope
- Check the LINE conditions for regression inference
- Construct and interpret confidence intervals for slope and mean response
- Construct and interpret prediction intervals for individual responses
- Distinguish between confidence and prediction intervals
Prerequisites
Before starting this module, you should be comfortable with:
- Calculating means and standard deviations (Module 2)
- Hypothesis testing concepts and procedures (Modules 8-10)
- Constructing confidence intervals (Module 7)
- Using t-distributions (Modules 7-10)
- Basic graphing and interpretation skills
Start Your Learning Journey
1. Pre-Assessment
Take a 5-question baseline assessment to measure your starting knowledge.
Start Pre-Assessment 5 questions2. Lessons
Complete four comprehensive lessons on linear regression and correlation.
4 lessons3. Practice
Work through 20 practice problems with detailed solutions.
Practice Problems 20 problems4. Quiz
Test your understanding with a 15-question auto-graded quiz (70% to pass).
Take Quiz 15 questions5. Post-Assessment
Measure your learning gains with a final 5-question assessment.
Post-Assessment 5 questionsLessons
Introduction to Linear Regression
25-30 minutes
Learn about bivariate data, scatter plots, correlation coefficients, and the relationship between two quantitative variables.
- Scatter plots and patterns
- Correlation coefficient (r)
- Properties of correlation
- Correlation vs causation
The Regression Equation
30-35 minutes
Master the least-squares regression line, including calculating slope and intercept, making predictions, and interpreting r².
- Regression equation: ŷ = b₀ + b₁x
- Calculating slope and intercept
- Residuals and standard error
- Coefficient of determination (r²)
Hypothesis Testing in Regression
30-35 minutes
Learn to test whether a significant linear relationship exists by testing correlation and slope, and check regression assumptions.
- Testing correlation (ρ = 0)
- Testing slope (β₁ = 0)
- LINE conditions
- Residual plots
Confidence & Prediction Intervals
25-30 minutes
Construct confidence intervals for slope and mean response, and prediction intervals for individual values.
- CI for slope
- CI for mean response
- Prediction intervals
- Confidence vs prediction
Study Resources
Study Guide
Comprehensive study guide with all formulas, procedures, and examples for Module 11.
View Study GuideQuick Reference
One-page quick reference card with essential formulas and interpretations.
View Quick Reference