Math 1 · Unit 10 · Lesson 1 · part 3 of 5
One number for direction and strength: r
Strength and direction can be packed into one number.
One number for direction and strength: r
Strength and direction can be packed into one number. The correlation coefficient, written r, is a number from −1 to 1 that measures how closely the points fit a line.
- 1The sign is the direction.Positive r: the points go up to the right. Negative r: they go down to the right.
- 2The size is the strength.r = 1 or r = −1 means every point is exactly on a line. Close to 1 or −1 is strong. Close to 0 is weak: no straight-line pattern.
| r | −1 | −0.9 | −0.5 | 0 | 0.5 | 0.9 | 1 |
|---|---|---|---|---|---|---|---|
| meaning | perfect line, going down | strong negative | moderate negative | no line at all | moderate positive | strong positive | perfect line, going up |
What does r = 0.97 tell you?Three things. The sign is positive, so the two quantities go up together. 0.97 is very close to 1, so the relationship is very strong. And because r measures fit to a line, a line fits this data well.
You do not compute r by hand. Technology does it, the same way a graphing calculator does. Build a scatter plot and watch r change as the points move.
A warning for later: r only measures how well a line fits. Points that follow a perfect curve can still give an r close to 1, and that can fool you into using a line. Lesson 3 shows how to catch it. For now: r is about lines, nothing else.