covariance and correlation

Question 1

name two measures of association

Answer 1

covariance and correlation

when looking for a single number to describe the relationship between two variables, you would presume that the joint probability would be enough but, if you need a deeper look you need covar and corr.

Question 2

how do you examine covariance for variables X and Y ?

Answer 2

you look at this

COV(X,Y) =
(X-meanx) . (Y-meany)

if its positive then they are both either + / -

if its negative one is + and one is -

Question 3

how do you calculate sample covariance ?

Answer 3

Sx,y = sum of ( (xi-smean) . (yi-smean) / n-1 )

Question 4

list some properties of covariance

Answer 4

can be altered by multiplication of a constant

COV(aX + c , bY + d)= abCOV(X,Y)

although it does reduce the usefulness as cov relies on scale

bounded by the product of the two variables standard deviations

Question 5

if X and Y are independent what is the covariance ?

Answer 5

COV = 0

Question 6

how do you calculate the correlation coefficient for

a. population
b. sample

Answer 6

a. CORR(X,Y) = cov/stdev1 .stdev2

b. samplecovar/ sx.sy

Question 7

list some properties of CORR?

Answer 7

invariant to units 
always same sign as COV
bounded by -1 and 1 
when corr=0, un correlated 
corr=1 perfectly positively 
corr=-1 perfectly negatively

Question 8

how do you use joint probability to test for independence ?

Answer 8

only independent when the joint probability = the product of the marginal probabilities

if X and Y are independent

E(XY) = E(X) . E(Y) and COV =0