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Unit 5 · Regression Analysis Flashcards Cheat Sheet Essentials Visual Review MC Practice FRQ Practice

AP Statistics Unit 5 Visual Review

A topic-by-topic visual walkthrough of Unit 5: Regression Analysis — scatterplots, correlation, least-squares regression lines, and residuals.

← Back to Unit 5 hub
TOPIC 5.1 Scatterplots explanatory (x) → response (y) Describe DUFS DIRECTION: positive / negative. UNUSUAL: outliers / influential points. FORM: linear / curved · STRENGTH: tight? Explanatory vs. response The EXPLANATORY variable (x) may help predict the RESPONSE (y). Association is not causation — see 5.2. Describe a scatterplot's Direction, Unusual features, Form, Strength. The Review Hub · AP Statistics Unit 5 TOPIC 5.2 Correlation r=−1−0.50+0.5r=+1 What r tells you r measures the STRENGTH & DIRECTION of a LINEAR relationship, −1 ≤ r ≤ 1. Near ±1 = strong linear; near 0 = weak. r has NO units and doesn't change if you swap x and y or rescale. Cautions • r only describes LINEAR patterns — a strong curve can have r ≈ 0. • r is NOT resistant to outliers. • CORRELATION ≠ CAUSATION. Always look at the scatterplot, not just r. −1 ≤ r ≤ 1 measures LINEAR strength/direction; correlation ≠ causation. The Review Hub · AP Statistics Unit 5 TOPIC 5.3 Linear Regression Models ŷ = a + b·x (predicted response) Interpret slope & intercept SLOPE b: predicted CHANGE in y for each 1-unit increase in x (with units!). INTERCEPT a: predicted y when x = 0 (may be meaningless out of range). ŷ = 3 + 2x → +2 in y per +1 in x ŷ is a PREDICTION The hat on ŷ means "predicted," not the actual observed value. EXTRAPOLATION (predicting far outside the x-range) is unreliable. Only predict within the observed data range. ŷ = a + b·x: slope b = predicted change in y per unit x; don't extrapolate. The Review Hub · AP Statistics Unit 5 TOPIC 5.4 Residuals residual ŷ line residual = y − ŷ Residual plots check the fit A residual = actual − predicted. Positive → the point is ABOVE the line. NO PATTERN in the residual plot → a line is a good model. A CURVED pattern → a line is NOT appropriate. residual = y − ŷ; a patternless residual plot means a line fits well. The Review Hub · AP Statistics Unit 5 TOPIC 5.5 Least-Squares Regression // the least-squares line minimizes Σ(residuals)² b = r · ( sᵧ / sₓ ) a = ȳ − b·x̄ the line always passes through the point (x̄, ȳ) The coefficient of determination r² r² = the PROPORTION of variation in y explained by the linear model. r² = 0.81 → "81% of variation in y is explained by x." s = standard deviation of residuals s is the typical PREDICTION ERROR — how far actual y's fall from the line, on average. Smaller s = a tighter, better fit. Read a, b, r, r², s from computer output. LSRL: b = r·(sᵧ/sₓ), a = ȳ − b·x̄; r² = fraction of y's variation explained. The Review Hub · AP Statistics Unit 5
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How to use the visual review

Spend 30 seconds per slide before clicking next. Look at the graph, then ask yourself: "Could I interpret this slope, judge this residual plot, or explain r² from memory?"

Use the fullscreen button () on desktop for the best experience. Use arrow keys to navigate. Tap "Show all slides" to jump around.

This is great for review the night before the exam — fast, visual, and covers every idea you need to recognize in Unit 5.