Корреляция

One number for a linear trend

• Correlation 相关性 $r$ is a single number for the strength and direction of a linear relationship.
• Its sign matches the direction: $r>0$ positive, $r<0$ negative.
• Its size measures tightness: near $\pm 1$ = tight line, near $0$ = no linear trend.
• $r$ turns "looks fairly strong" into a precise, comparable value.

Always between −1 and 1

• Correlation is bounded: $-1 \le r \le 1$, always.
• $r=+1$: a perfect increasing line; $r=-1$: a perfect decreasing line.
• $r=0$: no linear association (the points may still have a non-linear pattern).
• $r$ has no units and doesn't change if you switch which variable is $x$.

Positive correlation rises together; negative correlation moves in opposite directions

When r misleads

• $r$ measures linear strength only — a strong curve can give a middling $r$.
• A single outlier can pull $r$ up or down dramatically.
• So never report $r$ without first looking at the scatterplot.
• A high $r$ on a curved or outlier-driven plot is a false summary.

Correlation is not causation

• A large $r$ shows the variables move together, not that one causes the other.
• Ice-cream sales and drownings correlate — both rise in summer (heat is a lurking variable).
• Establishing cause needs an experiment, not just a high correlation.
• "Correlation does not imply causation" is the mantra of the whole unit.

Write from r equal to negative 0.9

• A scatterplot slopes downward and the points hug a line.
• The correlation is negative 0.9.