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* σyx )x

Regression equn 2:  x̄=(r2* σxy )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.