AP Stats 5A-5B Day 1 Visual Study Guide: Scatterplots, Correlation & Regression LinesAP Stats 5A-5B Day 1 Visual Study Guide: Scatterplots, Correlation & Regression Lines

Exploring Two-Variable Data

5A · Scatterplots 5A · Correlation r 5B · Prediction 5B · Residuals 5B · Slope & intercept

FRQ frames Cheat sheet

The one big idea: in Unit 1 you described one variable (shape, center, spread). Now you describe how two

quantitative variables move together (direction, form, strength), measure it with r, and then model it with a line ŷ = a

+ bx so you can predict y from x. 5B Day 1 is about using that line well: making predictions, measuring how far off

they are (residuals), and saying what the slope and intercept mean.

Relationships Between Two Quantitative Variables

2 0 - S E C O N D S U M M A R Y

The explanatory variable (x) may help predict or explain the response variable (y), which measures the outcome.

A scatterplot shows two quantitative variables for the same observational units, one dot per unit.

Describe it with DFSU: direction, form, strength, unusual features, in context.

r measures the strength and direction of a linear association only. It's between −1 and 1, has no units, and is not

resistant.

Correlation ≠ causation. Only a well-designed experiment shows cause and effect.

1 · Making a scatterplot

The packet's definition: a scatterplot shows the relationship between two quantitative variables measured for the same

observational units. The explanatory variable goes on the horizontal axis, the response on the vertical axis, and each

observational unit is one point.APS TAT ISTICS · UNIT5 · 5 A + 5BD AY 1 · M R . HANDY · TPS8 ESection 5A (scatterplots and correlation, both days) and 5B Day 1 (regression lines, prediction, residuals, slope and intercept), built from those three lecture slide decks and the Unit 5 notes packet. It matches what the 5A–5B Day 1

Quiz covers. Diagrams first, words second. Every interpretation sentence you'll need on an FRQ is here as a fill-in

frame.SECTION5 AScatterplots · describing association · correlation r · limits of r

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Hand span (cm) ← explanatory variable (x)

Number of candies (response, y)

one dot = one student

(21 cm, 33 candies)

Label BOTH axes with units

Scale evenly (equal gaps)

Anatomy of a scatterplot. Explanatory variable on the horizontal axis, response on the vertical axis, one point per observational unit (here, per student). On the AP exam, an unlabeled or unscaled axis costs credit. Which variable is explanatory? Ask "which one would I use to predict the other?" In the slides' coral example, depth is explanatory because it might help explain corallite density. Sometimes there's no clear choice (e.g., math and reading scores). Then either can go on x.

AP Exam Tip (from the slides)

If you're asked to construct a scatterplot, label and scale both axes. Don't just copy an unlabeled calculator graph onto your paper.

QUICK CHECK

A researcher records the age (years) and resale value (dollars) of 30 used bikes. Which goes on the x-axis? Answer: Age. It's the explanatory variable: we'd use age to predict value, not the other way around. 2 · Describing a scatterplot: DFSU

Positive association: values of one variable tend to increase as the other increases.

Negative association: values of one variable tend to decrease as the other increases.

No association: knowing one variable doesn't help predict the other (the slides' height vs. Saturday sleep).

D · Direction

Positive Negative No association

F · Form

Linear Nonlinear (curved) Nonlinear (bend)

S · Strength

Strong Moderate Weak

U · Unusual features

Outlier (red) Clusters

The four things every scatterplot description needs: DFSU. Strength is about how closely the points hug the form, not how steep the pattern is.

S E N T E N C E F R A M E : DESCRIBE

There is a [strong / moderate / weak], [positive / negative], [linear / nonlinear] relationship between [x in context] and [y in context] for [the observational units]. [Name any outlier with its approximate values and say why it's unusual, or say there are no unusual features.]

Slides' model answer (graduation rates): "There is a weak, negative, linear relationship between the statewide graduation rate (%) and student-to-faculty ratio for the colleges and universities in each state and Washington, D.C. There is a state outside this pattern with an average of about 9.1 students per faculty member and a graduation rate of about 37%, which is much lower than expected." Notice it names the units (states + D.C.), gives the outlier's coordinates, and says why it's unusual.

TRAP TO AVOID

Saying "strong" because the pattern is steep. Strength is about scatter: how tightly points follow the form. A nearly flat line of points packed tightly together is strong; a steep cloud is weak.

TRAP TO AVOID

Saying a positive association means every larger x has a larger y. The slides: direction describes only the overall trend, not an absolute relationship. In the WNBA plot, some tall players still shoot free throws well.

QUICK CHECK

Data: 41 League of Legends players, gold earned per minute vs. damage per minute. The points rise tightly along a line with nothing off-pattern. Describe it.

Answer: There is a strong, positive, linear relationship between damage per minute and gold per minute for the 41 LCS players, with no outliers or other unusual features.

3 · Correlation r

When the association is linear, the correlation r measures its strength and direction. The properties the slides list: What r tells you

−1 ≤ r ≤ 1

Sign = direction (r > 0 positive, r < 0 negative)

Close to ±1 = strong linear; close to 0 = weak

linear

r = ±1 only if every point is exactly on a line

Facts about r

Both variables must be quantitative. Otherwise say

"association"

Swapping x and y gives the same r

Changing units (cm → in, $ → ¢) doesn't change r

r has no units (it's built from z-scores)

r = −1 r = −0.8 r = −0.5 r = 0 r = 0.5 r = 0.8 r = 1

−1 perfect negative 0 no linear association perfect positive +1

What different values of r look like. Every plot here has exactly the r shown. Notice that r = 0.5 still looks like a mess. Most people overestimate how strong a moderate r looks.