Unit 5: Regression Analysis
Unit 5 is 10–20% of the AP Statistics exam. In the 2026–27 redesign, inference for slopes was removed — Unit 5 is now purely descriptive and predictive regression. The exam expects you to read scatterplots and residual plots, interpret computer output, and make predictions using the least-squares regression line.
Weight and scope
Exam weight: 10–20%. Every AP Statistics exam has at least one MCQ block on regression output interpretation, and a regression FRQ appears roughly every other year.
Topic list (2026–27 CED)
- Representing bivariate quantitative data with scatterplots
- Correlation coefficient r — properties and interpretation
- The least-squares regression line (LSRL)
- Residuals and residual plots
- Coefficient of determination r²
- Using the LSRL to predict; interpolation vs. extrapolation
- Influential points, outliers, and high-leverage points
- Reading computer regression output
What was removed
- Departures from linearity as its own topic (old 2.9) — you still check linearity via a residual plot.
- Inference for the slope of a regression line — the entire old Unit 9 is gone. You no longer construct a t-interval for β or run a t-test on the slope.
The interpretations you must know cold
| Quantity | How to interpret in context |
|---|---|
| Slope b | For each additional unit of x, the predicted y increases (or decreases) by b units, on average. |
| y-intercept a | The predicted value of y when x = 0 (state whether this is meaningful in context). |
| Correlation r | The direction and strength of the linear association between x and y. Always between −1 and 1. |
| r² | About r²·100% of the variation in y is explained by the linear regression on x. |
| Residual | Observed y minus predicted y. Positive → LSRL underpredicted; negative → overpredicted. |
| s (residual SD) | The typical size of a residual — how far a prediction is off, on average, in the units of y. |
Reading a residual plot
- Random scatter around 0 → linear model is appropriate.
- Clear curve → linear model is not appropriate; a transformation is needed.
- Fanning out → non-constant variance; predictions are less reliable for larger x.
Reading computer output
The exam expects fluency with Minitab-style regression output. Given a table with rows for the intercept and slope and columns for Coef, SE Coef, T, and P — you should be able to write the equation of the LSRL, identify s and r², and state predictions.
Common mistakes
- Interpreting slope without "on average" or without units.
- Confusing correlation with causation.
- Extrapolating far outside the observed range of x.
- Reporting r² as a percent without saying "of the variation in y."
- Attempting inference on the slope — no longer part of the course.
FAQ
Is inference for slopes still on the AP Statistics exam?
What does the r² value tell me?
Keep going
Master regression interpretation for FRQ 4.
Cramapple's regression practice grades interpretation sentences the way AP graders do — 'on average,' units, and context all count.