Key ideas & terms
Prefer to read? Here's the lesson at a glance.
Key ideas
- Scatter plots show the relationship between two quantitative variables, with each participant becoming one dot.
- The correlation coefficient (r) ranges from -1 to +1: the sign shows the direction of the relationship, and the distance from zero shows its strength.
- A correlation is perfect (+1 or -1) when every point lands exactly on a straight line, whether that line is steep or shallow.
- The closer the points are to a straight line, the stronger the correlation; the more scattered they are, the weaker it is.
- No matter how strong a correlation is, it never proves that one variable caused the other.
Key terms
- scatter plot
- A graph that shows the relationship between two quantitative variables, with each participant plotted as one dot.
- positive correlation
- As one variable increases, the other also tends to increase; dots slope upward.
- negative correlation
- As one variable increases, the other tends to decrease; dots slope downward from left to right.
- correlation coefficient (r)
- A number from -1 to +1 showing how strongly two variables are correlated and whether the correlation is positive or negative.
- perfect correlation
- A correlation of +1 or -1, where every point falls exactly on a straight line, so one variable perfectly predicts the other.
- zero correlation
- A correlation coefficient of 0, where points show no clear upward or downward trend.
Watch out
Strength comes from how tightly points hug the line, not how steep the line is; -0.75 is a stronger correlation than +0.25.
Correlation never proves causation, no matter how strong. (You won't calculate r on the AP exam, but you must interpret it.)