Question

Describing Correlation
Explain what it means to have a correlation in a scatterplot.

Answer 1

A correlation in a scatterplot describes a consistent relationship between the x and y values shown as the pattern of points.

Key ideas:
- Direction:
- Positive correlation: points trend upward left-to-right (as x increases, y tends to increase).
- Negative correlation: points trend downward left-to-right (as x increases, y tends to decrease).
- No correlation: points are scattered with no clear upward or downward trend.
- Strength:
- Strong correlation: points lie close to a single line or curve (little scatter).
- Weak correlation: points are widely scattered around the trend (lots of variability).
- Form:
- Linear correlation: points cluster around a straight line.
- Nonlinear (curvilinear) correlation: points follow a clear curve; a straight-line correlation measure may be misleading.
- Numerical measure: the Pearson correlation coefficient r (range −1 to +1) summarizes linear correlation: r ≈ +1 (perfect positive), r ≈ −1 (perfect negative), r ≈ 0 (no linear correlation).
- Important caveat: correlation does not imply causation. Two variables can be correlated because of coincidence, a hidden third variable, or a direct causal link — you cannot conclude cause from correlation alone.
- Outliers can strongly affect the apparent correlation and the numeric r value.

In short: a correlation means the points show a consistent pattern relating x and y in direction and strength; how tightly they follow a line or curve determines how strong that relationship is.