Scatter Plots
A scatter plot shows how two variables move together. Each observation
contributes one pair (x, y), drawn as a single dot:
x sets how far right it sits, y how far up.
Plot the whole sample and the cloud of dots reveals the relationship between the
two variables at a glance.
One dot per observation — so a class of 30 students, each measured for
height x and shoe size y, becomes
30 dots. Nothing is summarised away; you see every individual and the
overall shape at the same time.
Direction and shape
Two questions read straight off the picture.
-
Direction. If the dots drift upward to the right — large
x with large y — the association is
positive. If they drift downward — large
x with small y — it is
negative. A shapeless blob with no consistent tilt shows
no association.
-
Shape. If the dots hug a straight path the relationship is
linear; if they follow a bend or a U the relationship is
curved (nonlinear).
Switch between three clouds
Flip the control to compare a positive cloud (rising to the right), a
negative cloud (falling to the right), and a cloud with no
association (a shapeless scatter). The same axes hold all three, so only the
tilt of the dots changes.
Association is not causation
A scatter shows that two variables move together — it does not show that
one causes the other. Ice-cream sales and drowning deaths both climb in summer, so they
form a tidy positive scatter, yet neither causes the other: a third, lurking
variable — the heat — drives both. A pattern in the dots is a starting point for investigation,
never a proof of cause.
- A scatter plots one dot per observation at its pair (x, y).
- Direction: rising dots = positive, falling dots = negative, a shapeless blob = no association.
- Shape: dots near a straight path are linear; a bend or U is curved.
- An association is not a cause — a lurking variable can drive both.