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Scatterplots & correlation
Same idea, four ways to study it. Tap a style and find the one that clicks for you. 📺 Prefer to watch? Videos are on the lesson page.
📉 Describe any scatterplot in 4 words: form, direction, strength, outliers. Then Pearson's r (a number from −1 to +1) puts a figure on the direction and strength.

What it is

When you have two sets of numbers (like training hours and goals scored), a scatterplot lets you see whether one is related to the other. The explanatory variable goes on the x-axis (the one doing the predicting), the response on the y-axis.

Describe any scatterplot in 4 words

Form
Linear (a straight-line pattern) or non-linear (curved)?
Direction
Positive (up), negative (down), or none.
Strength
How tightly do the points hug the line? Strong, moderate, weak.
Outliers
Any points that don't fit, mention them.

Pearson's r, the correlation coefficient

Your calculator gives r, a number from −1 to +1. The sign tells you the direction, the size tells you the strength.

r near…Means
+1strong positive
0no linear correlation
−1strong negative

Worked example

8 strikers: training sessions/week (x) vs goals/season (y). The calculator gives r = 0.99.

  1. Variables: x = training sessions (explanatory), y = goals (response).
  2. Describe: points go up to the right (positive), follow a straight line (linear), cluster tightly (strong), no outliers.
  3. Interpret r = 0.99: very close to +1 → a very strong, positive, linear association between training sessions and goals.

Watch out

• Correlation is not causation. A strong r means the two move together, not that one causes the other.
• r only measures linear association, a perfect curve can still have a low r.
• Always describe in context (name the variables), "strong positive" alone won't get full marks.
• An outlier can pull r up or down, flag it.

The three directions

positive (r > 0) negative (r < 0) none (r ≈ 0)

Up to the right is positive, down to the right is negative, no pattern means r near zero.

The r scale

−1 0 +1 strong neg none strong pos

The closer r is to either end, the stronger the linear relationship. The middle means no linear pattern.

Warm up first

Don't read yet, just have a go in your head:

"Training hours predict goals." Which is the explanatory variable?
Training hours (it does the predicting, so it's x). Goals is the response (y).
r = −0.9. Direction and strength?
Strong negative. The minus sign is the direction, 0.9 (close to 1) is the strength.
What are the 4 words to describe a scatterplot?
Form, direction, strength, outliers.

Faded example: 8 strikers, r = 0.99

Rung 1 · watch one done fully

Points go up to the right (positive), straight-line pattern (linear), tight cluster (strong). r = 0.99 → very strong positive linear association.

Rung 2 · you fill the gaps

r = 0.99 is close to ?, so the association is ? and ?.

Check my gaps
close to +1, so strong and positive (and linear).
Rung 3 · all you

A study finds r = −0.15 between hours of TV and exam marks. Describe the association in words. Check below.

Check my answer
r = −0.15 is close to 0, so there is a weak (almost no) negative linear association between hours of TV and exam marks.

Exam-style stretch: causation

Ice cream sales and drownings both rise together (high r). Does buying ice cream cause drownings? Explain.

Show the answer
No. A high correlation only means they rise together. A third factor, hot weather, drives both up. Correlation does not prove causation, there can be a lurking variable.

Say it back

In one sentence, out loud: what do the sign and size of r each tell you? If you can say it, you've got it.

⚡ Scatterplots & correlation, one look

Explanatorythe x variable (does the predicting)
Responsethe y variable (the outcome)
Describe in 4form · direction · strength · outliers
Pearson's r−1 to +1 · sign = direction · size = strength
Strongr near +1 or −1 · weak: r near 0
Exampler = 0.99 → very strong, positive, linear
Trapcorrelation ≠ causation · r only measures linear