Unit 5 Regression Analysis

Unit 5 Videos:

Unit 5 Lessons

Welcome to AP Statistics Unit 5!

Welcome to Unit 5: Regression Analysis, where we explore relationships between two quantitative variables. In this unit, you’ll learn to describe how variables are associated, measure the strength and direction of those relationships, and use least-squares regression to make predictions.

More importantly, you'll learn how to interpret your results in context — something that separates true statistical thinking from simply pressing buttons on a calculator. Students investigate patterns, identify linear and nonlinear associations, analyze residuals for appropriateness of linear models, and understand what information technology output actually communicates.

Key Concepts Covered

Scatterplots & Associations: Construct scatterplots and describe form, direction, strength, and unusual features in bivariate data.
Correlation: Interpret the correlation coefficient r as a measure of direction and strength of a linear relationship, while recognizing that correlation does not imply causation.
Linear Regression Models: Use technology to obtain a least-squares regression line, calculate predicted values, and understand interpolation vs. extrapolation.
Residuals & Model Fit: Compute residuals, interpret them in context, and use residual plots to assess whether a linear model is appropriate. Random scatter supports linearity; curved patterns do not.
Coefficient of Determination r^2: Interpret r^2 as the proportion of variation in the response variable explained by the linear relationship with the explanatory variable.

Mr. Antonucci’s Expert Tips for Unit 5

“One of the biggest mistakes students make in Unit 5 is treating correlation and regression as purely mechanical processes. It’s not enough to calculate the regression line — you must interpret what the slope, intercept, residuals, and r^2 mean in context. Students also tend to forget to check whether a linear model is even appropriate in the first place. A residual plot can make or break your conclusions, so don’t skip it!”