__Co-Efficient of Linear Correlation__

__of __

__Ungrouped scores __

__( by taking deviations from
the mean )__

Formula-1
: r = Σ**xy**
**/** **√ (Σx ^{2} * Σy^{2})**

**
**where x=X_{i} -X_{mean} and y =Y_{i} -Y_{mean} and i is the ith entry with value
varying between 1 to 15 here.

Formula-2;Difference Formula : r1 = ( Σ**x**^{2}**+**Σ**y**^{2}-Σ**d**^{2}
)** /** ** [ 2*√ (Σx ^{2} * Σy^{2 }) ] **
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/σ_{x})*(y/σ_{y})])
/ N

Regression equn 1: ȳ=(r2* σ_{y}/σ_{x}
)x

Regression equn 2: x̄=(r2* σ_{x}/σ_{y}
)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.