Co-Efficient of Linear Correlation

of

Ungrouped scores

( by taking deviations from the mean )

no. of subjects-- (N)  Test-1 Test-2
SUBJECT X Y
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
     
* Fill in no. of subjects - Here it can be any no. between 1 to 15. X and Y should have equal no. of entries.

* X and Y should be filled up serially from top to down. No in between column should be blank.

     

   
Mean X  
Mean Y  
SD(X)->σx *
SD(Y)->σy *
Co-efficient of correlation by difference formula (r1)  
Co-efficient of correlation (r)  
Co-efficient of correlation(r2)
First Regression Equn -- y=x y=x
Second Regression Equn-- x=y x=y
     

                 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.