Plot every student as a dot — study hours across, exam score up. If the cloud of dots slopes upward, you've spotted a relationship. Scatter plots are how you *see* whether two things move together.
A scatter plot shows two variables at once: each data point is a dot at (x, y). The pattern of the cloud reveals whether — and how — the variables are related.
The first step in any two-variable investigation: correlation, regression, spotting clusters and outliers, checking for non-linear shapes before trusting a straight-line fit.
y ≈ 1x + 0.75
r runs from −1 (perfect down) through 0 (no link) to +1 (perfect up). Correlation isn't causation!
Patterns to read off
- Upward cloud → positive relationship (both rise together).
- Downward cloud → negative relationship.
- Shapeless blob → little or no relationship.
- Curved band → non-linear relationship — a straight-line fit would be wrong.
- Lone far-off dots → outliers to investigate.
A scatter plot of dots forms a tight upward line. Roughly what correlation r would you expect?
Why look at the scatter plot *before* computing a correlation coefficient?
r only measures *linear* association. A perfect U-shaped relationship has r ≈ 0 — the scatter plot would scream 'strong relationship!' while r whispers 'nothing here'. Always eyeball the cloud first.
A pattern in a scatter plot is correlation, never proof of causation. And r ≈ 0 doesn't mean 'no relationship' — only 'no *linear* one'. Look at the actual shape.
After spotting an upward/downward trend, the natural next step is least-squares regression — drawing the line of best fit through the cloud.
- Each dot is an (x, y) pair; the cloud's shape shows the relationship.
- Upward / downward / blob / curve / outliers — learn to read each.
- Shows association, not causation; check the shape before trusting r.