Correlation

Definition:

• Refers to any broad class of statistical relationships involving dependence
• The correlation of two random variables $X$ and $Y$, denoted by $\rho (X,Y)$
  • defined as long as $Var(X).Var(Y)$ is positive
  • Denotes the degree of linearity:
    • Near +1 or -1 denotes there is a high degree of linearity
    • Near 0 indicates such linearity is absent

Correlation Coefficient

Coefficient of Determination:

• Square of the Correlation Coefficient, ${\rho }^2$
• Measures the explanatory power (the strength) of the regression model.
• Meaning ${\rho }^2\ast 100\%$ of $y$ depends on $x$

Degrees of correlation:

• Perfectly Correlated
  • Perfect positive vs perfect negative correlation
  • Has no margin of error
• Partly Correlation
• Uncorrelated

Spearman’s Rank Correlation Coefficient