How does the nature of the dependent variable vary based on the independent variable ? – This is explained by taking a sample of the population and computing Covariance.
This just shows if the two variables are positively related (or) negatively related (or) not related at all.
Assuming x is independent and y as dependent, have a number of observations and plot scatter diagrams for visual view.
Covariance = Sum of (( x – x bar) ( y – y bar)) / (n-1)
For Covariance to be applicable cov(x,y) = cov(y,x) and Cov(x,x) = variance (x).
The sample correlation coefficient is derived from sample Covariance so it can be used as a unitless measure to compare apples to apples.
Correlation Coefficient = Cov(x,y) / std x . std y
std x = sqrt(sum(x – x bar)/ n-1 )