In: Statistics and Probability
For each of the following scenarios A and B:
Scenario A |
Scenario B |
|
COV(X,Y) |
155 |
-480 |
Standard deviation of X |
50 |
242 |
Standard deviation of Y |
50 |
2 |
Scenario A |
Scenario B |
|
Covariance |
COVA (X,Y) = 155 |
COVB (X,Y) = - 480 |
Standard deviation of X |
σXA = 50 |
σXB = 242 |
Standard deviation of Y |
σYA = 50 |
σYB = 2 |
Correlation between X and Y |
ρA(X,Y) = 0.062 |
ρB(X,Y) = - 0.9917 |
For scenario A:
Correlation between X and Y = ρA(X,Y) = COVA (X,Y) / σXA∙σYA
= 155 / 50 ∙ 50
ρA(X,Y) = 0.062
For scenarion A, the value of Correlation between X and Y is A weak positive linear relationship through a shaky linear rule.
For scenario B:
Correlation between X and Y = ρB(X,Y) = COVB (X,Y) / σXB ∙ σYB
= - 480 / 242 ∙ 2
ρB(X,Y) = - 0.9917
For scenarion B, the value of Correlation between X and Y is A strong negative linear relationship through a firm linear rule.
r = 0 |
No linear relationship or no linear correlation |
r = + 1 |
A perfect positive linear relationship – as one variable increases in its values, the other variable also increases in its values through an exact linear rule. |
r = - 1 |
A perfect negative linear relationship – as one variable increases in its values, the other variable decreases in its values through an exact linear rule. |
r = 0 to r = 0.3 |
A weak positive linear relationship through a shaky linear rule. |
r = 0 to r = - 0.3 |
A weak negative linear relationship through a shaky linear rule. |
r = 0.3 to r =0.7 |
A moderate positive linear relationship through a fuzzy-firm linear rule. |
r = - 0.3 to r = -0.7 |
A moderate negative linear relationship through a fuzzy-firm linear rule. |
r= 0.7 to r= 1 |
A strong positive linear relationship through a firm linear rule. |
r = - 0.7 to r = - 1 |
A strong negative linear relationship through a firm linear rule. |