- Sample Space
- all undergraduate at Queen's
- amount of outside study time put in by student (per day)
- overall average marks of the student
Covariance extends The notion of variance to two dimensions. Its value measures the linear relationship between r.v. Positive covariance indicates that when X is above its mean then Y tends to be above its mean as well - positive statistical relationship. Negative covariance indicates that when X is above its mean Y tends to be below its mean - negative statistical relationship
- Correlation between two random variables ( ) is defined as
( is a common synonym for corr).
Note that Cov[X,2Y] = 2Cov[X,Y], so a simple linear change in the random variables will increase or decrease the size of their covariances. Correlation avoids this scaling effect.
The absolute value of corr[X,Y] measures the degree of linear relationship between them. The sign of corr[X,Y] indicates whether there is a positive or negative relationship between X and Y. Unlike covariance, correlation is unaffected by the scaling of the random variables by constants.
f (x) f(x,y) 0 1 X -------------------- 1 | 0.1 | 0.3 | 0.4 |_________|__________| | | | 2 | 0.4 | 0.2 | 0.6 --------------------- f (y) 0.5 0.5 1.00 Y