Before any formula, a scatterplot is something you read with your eyes, and there is a fixed order to it: form first — is the cloud a straight line, a curve, or no shape at all? Then direction — does it drift up to the right or down? Then strength — do the points hug the pattern tightly or scatter loosely around it? Only after those three does a number, the correlation, earn a place. Below you get to set the relationship, then draw a real sample from it point by point. Watch the correlation move as you loosen and tighten the cloud — and watch what it does when the form is a curve, where a single number quietly stops telling the truth.
One sample of paired measurements
Each dot is one subject measured on two things — its x on the horizontal axis, its y on the vertical. The pale dashed guide is the true pattern you set on the right; the solid teal line is the least‑squares line fitted to these actual points. Press Draw another sample to collect a fresh set of subjects from the same relationship and see how much the picture — and the correlation — jump around.
your samplefitted line (from the dots)true pattern (what you set)
Say it right
Eight things people say when reading a scatterplot. Four are sound and four are traps. Tap each to check yourself.
The section in one lineRead a scatterplot in three moves — form, direction, strength — and never let the correlation jump the queue, because it only measures the linear part of the story and is blind to everything else.
A cloud of dotsshape it, then go sampling
Shape the relationship
Set the truth behind the dots, then read it back off the picture. In real data you never get to set these — you have only the scatterplot — so practise seeing each choice in the cloud it produces.
Form — the overall shape
Direction — which way it leans
Strength — how tightly it hugs the pattern
0.75
How many subjects
70
Jump to a picture worth seeing
This sample, read three ways
Form (judge by eye)—
Direction (sign of the tilt)—
Correlation r—−1 to +1
Strength (from |r|)—
0weakmoderatestrong1
What to carry out of this section
Form, then direction, then strength — in that order. Direction and strength are only meaningful once you have named the form. Calling a cloud “weakly positive” when it is actually a clean U‑shape is not a small mistake; it throws away the entire shape of the relationship. Always answer “what is the form?” before you let yourself say anything about how strong it is.
The correlation only sees straight lines. Load The curve trap. The points trace an obvious, tight U — a relationship so strong you could almost draw it freehand — yet r sits near zero, because r measures only how well a straight line fits. A correlation near zero never means “no relationship”; it means “no linear relationship,” and those are very different claims. This is exactly why the scatterplot comes first and the number comes second.
A pattern is not a cause. A tight, unmistakable correlation still says nothing about why the two variables move together — a third variable may drive both, or the arrow may point the other way. The scatterplot describes an association; deciding what produced it is a question about how the data were collected, and no value of r, however close to 1, can answer it.
One more habit worth building: strength is about how tightly the points cling to the pattern, not how steep the line is. Set a strong positive line, then look only at the spread around the fitted line, not its slope. A nearly flat line can be a strong relationship, and a steep line can be a weak one — slope and strength are two different questions, and only the second is what r reports.