Co-Efficient of Linear Correlation
( by taking deviations from the mean )
Formula-1 : r = Σxy / √ (Σx2 * Σy2)
where x=Xi -Xmean and y =Yi -Ymean and i is the ith entry with value varying between 1 to 15 here.
Formula-2;Difference Formula : r1 = ( Σx2+Σy2-Σd2 ) / [ 2*√ (Σx2 * Σy2 ) ] where d = x-y
* When sample size is less than 30, while calculating SD i.e. standard deviation, (N-1) is taken in stead of N
Formula-3 :r2= (Σ [(x/σx)*(y/σy)]) / N
Regression equn 1: ȳ=(r2* σy/σx )x
Regression equn 2: x̄=(r2* σx/σy )y
Although both the Regression equations involve x & y, the two equations cannot be used interchangeably nor can be used to predict both x & y.
* The Equn 1 can be used only when y is to be predicted from a given x i.e. y is dependent variable.
* The Equn 2 can be used only when x is to be predicted from a given y i.e. x is dependent variable.
Only when correlation is 1, both the equations become identical.