Taking one aspirin per day may decrease your chances of stroke or of a heart attack.
Eating lots of certain kinds of fish may improve your health and make you smarter.
Driving slower reduces your chances of getting killed in a traffic accident.
Taller people tend to weigh more.
Pregnant women that smoke tend to have low birthweight babies.
Animals with large brains tend to be more intelligent.
The more you study for an exam, the higher the score you are likely to receive.
Discipline | r meaningful if | R_{2} meaningful if |
---|---|---|
Physics | r < -0.95 or 0.95 < r | 0.9 < R^{2} |
Chemistry | r < -0.9 or 0.9 < r | 0.8 < R^{2} |
Biology | r < -0.7 or 0.7 < r | 0.5 < R^{2} |
Social Sciences | r < -0.6 or 0.6 < r | 0.35 < R^{2} |
x | 1 | 3 | 4 | 5 | 7 |
---|---|---|---|---|---|
y | 5 | 9 | 7 | 1 | 13 |
y = (5 + 9 + 7 + 1 + 13) / 5 = 7
SD_{x}^{2} = [(1-4)^{2} + (3-4)^{2} + (4-4)^{2} + (5-4)^{2} + (7-4)^{2}] / 5 = 4
SD_{x} = √4 = 2
SD_{y}^{2} = [(5-7)^{2} + (9-7)^{2} + (7-7)^{2} + (1-7)^{2} + (13-7)^{2}] / 5 = 16
SD_{y} = √16 = 4
x | y | z_{x} | z_{y} | z_{x}z_{y} |
---|---|---|---|---|
1 | 5 | -1.5 | -0.5 | 0.75 |
3 | 9 | -0.5 | 0.5 | -0.25 |
4 | 7 | 0.0 | 0.0 | 0.00 |
5 | 1 | 0.5 | -1.5 | -0.75 |
7 | 13 | 1.5 | 1.5 | 2.25 |
Ave. of z_{x}z_{y}: 0.40 |
x | 1 | 3 | 4 | 5 | 7 |
---|---|---|---|---|---|
y | 5 | 9 | 7 | 1 | 13 |
x | y | z_{x} | z_{y} | z_{x}z_{y} |
---|---|---|---|---|
1 | 5 | -1.34164 | -0.44721 | 0.60 |
2 | 9 | -0.44721 | 0.44721 | -0.20 |
3 | 7 | 0.0 | 0.0 | 0.00 |
4 | 1 | 0.44721 | -1.34164 | -0.60 |
5 | 13 | 1.34164 | 1.34164 | 1.80 |
Ave. of z_{x}z_{y}: 0.32 |