Page 209 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes Cov(X ,Y )
Correlation co-efficient () = i i
{V(X )V(Y )}
i
i
 (X  X)(Y  Y)
i
i
where Cov(X ,Y ) =
i i
n
 (X  X) 2
i
and V(X ) =
i
n
 (Y  Y) 2
V(Y ) = i
i
n
 xy
 =
 x 2  y 2

Where x  X  X and y  Y  Y
i i
Pearson’s Method – Direct Method

We apply direct formula to find Karl Pearson’s Co-efficient of correlation.

Example 1: Following is the data on two variables X and Y we find the sums and squares
i i
of products as shown in the table below:

( X  X ) ( Y  Y ) ( X  X ) 2 ( Y  Y ) 2 ( X  X )( Y  Y )
i
X i Y i i i i i i
2
2
x y x y xy

2 7 -2 - 4 4 16 8
3 9 -1 - 2 1 4 2
4 10 0 - 1 0 1 0
5 14 1 3 1 9 3
6 15 2 4 4 16 8

20 55  x =10  y =46  xy = 21
2
2

 X i 20  Y i 55
X =   4, Y    11
n 5 n 5

 xy
 =
 x 2  y 2

21 21
 =  = 0.98
10 46 3.16 x 6.78
The value of  = 0.98 shows that two series X and Y have almost perfect positive correlation.

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