A scatterplot shows paired data — each dot is one observation with an x-value and a y-value — and its overall drift tells you how the two variables move together. When the cloud rises left-to-right, the variables are positively correlated (more of one goes with more of the other); when it falls, they are negatively correlated; when the dots are a shapeless blob, there is little or no correlation. The GRE sometimes names the correlation coefficient r, a number that lives between −1 and +1: values near +1 mean a tight up-sloping line, near −1 a tight down-sloping line, and near 0 no linear pattern. The single most tested idea here is a caveat, not a formula: correlation is not causation. Two things can rise together because a third factor drives both, so a strong r never by itself proves that one variable causes the other. Also beware a single outlier dragging a line — real GRE scatter questions reward reading the trend, not overfitting one stray point.
✅ Solved examples
1. A scatterplot of hours studied (x) versus exam score (y) shows dots rising from lower-left to upper-right. Describe the correlation.
The cloud slopes upward, so more study hours go with higher scores: a positive correlation (r > 0).
2. A plot of outdoor temperature (x) versus heating-bill amount (y) trends downward as temperature rises. What is the sign of r?
Higher temperature goes with a lower bill — the trend falls, so the correlation is negative, r < 0.
3. Correlation coefficients for four data sets are −0.9, −0.2, 0.1, and 0.8. Which set has the strongest linear relationship?
Strength is the distance from 0 (the absolute value), not the sign. |−0.9| = 0.9 is the largest, so r = −0.9 is the strongest linear relationship.
4. A study finds a strong positive correlation between ice-cream sales and drowning incidents. Does buying ice cream cause drownings?
No. Correlation is not causation. A third variable — hot summer weather — increases both swimming and ice-cream buying, producing the correlation without any direct cause between them.
✏️ Practice — try these, take hints as needed
1. Dots on a scatterplot fall steadily from upper-left to lower-right. Positive or negative correlation?
Read the direction of the trend.
Falling means as x grows, y shrinks.
That is the negative case.
Negative
2. Which is stronger: a correlation of r = −0.85 or r = 0.6?
Ignore the sign for strength.
Compare absolute values.
0.85 vs 0.6.
r = −0.85
3. A scatterplot is a round, shapeless cloud with no tilt. What is r approximately?
No linear trend at all.
Neither up nor down.
r is near this value.
About 0
4. City data show more firefighters at a blaze correlate with greater fire damage. Do firefighters cause damage?
Ask what drives both numbers.
Bigger fires summon more crews.
Correlation is not causation.
No — fire size drives both
5. Can a correlation coefficient equal 1.4?
Recall the fixed range of r.
r lives between two limits.
The maximum is +1.
No — r cannot exceed 1
📝 Topic test — 8 questions
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