- To measure the degree of linear dependence between two variable, Pearson Product Moment Correlation Coefficient (PPMCC) is used. This coefficient was developed by Carl Peasron.
- This coefficient gives Statistical measurement of linear relationship between paired data.
- This coefficient is denoted by 'r' and it is in the range, -1 ≤ r ≤ +1.
- If value of 'r' is positive, then it gives positive linear correlation.
- If value of 'r' is negative, then it gives negative linear correlation.
- And if r = 0, then it indicates that there is no linear correlation.
- The range of 'r' is from -1 to +1, so if the value of r is closer to +1 or -1 then it indicates stranger positive and negative linear correlation.
- When the Pearson's correlation coefficient is applied to population then it is called as population pearson correlation coefficient and it is denoted by ρ (rho).
- This coefficient is given by,
ρx,y = COV (X, Y) / σx . σy ...(1)
Here, COV(X,Y) denotes the covariance between X and Y.
σx and σy denotes standard deviation of X and Y respectively.
Here, COV(X,Y) denotes the covariance between X and Y.
σx and σy denotes standard deviation of X and Y respectively.
- In terms of expectations (E), equation (1) can be written as,
ρx,y = E(X, Y) - E(X).E(Y)
√E(X2) - E(X)2 . √E(Y2) - E(Y)2
- Consider that, we have the data sets (x1 , x2 , x3 , ..., xn ) and (y1 , y2 , y3 , ...yn ), contain n samples then the correlation coefficient is denoted by r and it is given by,
- Here x̄ and ȳ denote the sample mean and given by,
x̄ = 1 Σxi and ȳ = 1 Σyi (from i = 1 to n)
n n