Page 162 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes Example 6: Compute Karl Pearson’s correlation coefficient for the data given below:

X : 45 55 56 58 60 65 68 70 75 80 85

Y : 56 50 48 60 62 64 65 70 74 82 90

Solution: Since means of X and Y are in fractions we will apply the assumed mean method of
calculating correlation. Taking 65 as the assumed mean in case of X and 66 in case of Y:

Calculation of Coefficient of Correlation
X (X – 65) d x 2 Y (Y – 66) d y 2 dd
x y
d x d y

45 – 20 400 56 – 10 100 + 200
55 – 10 100 50 – 16 256 + 160
56 – 9 81 48 – 18 324 + 162
58 – 7 49 60 – 6 36 + 42
60 – 5 25 62 – 4 16 + 20
65 0 0 64 – 2 4 0
68 + 3 9 65 – 1 1 – 3
70 + 5 25 70 + 4 16 + 20
75 + 10 100 74 + 8 64 + 80
80 + 15 225 82 + 16 256 + 240
85 + 20 400 90 + 24 576 + 480

2
∑X = 717 ∑d = +2 ∑d x 2 = 1414 ∑Y = 721 ∑d = – 5 ∑d y = 1649 ∑dd = 1401
y
y
x
x
( x )∑ ( d d y ) ∑
∑dd y –
x
r = 2 N ( 2
∑ x – ( 2 N x )∑d ∑d d y 2 – N y ) ∑d

∑dd y = 1401, ∑d = + 2, ∑d = – 5, ∑d x 2 = 1414, ∑d y 2 = 1649, N =
x
x
y
11
()( )
2–5
1401 –
r = 11
() 2 2 ( )–5 2
1414 – 1649 –
11 11
1401.91
=
1414 –.364 1649 – 2.273

1401.91 1401.91 1401.91
= = = = +
1413.636 1646.727 37.598 × 40.5799 1525.723
0.919
Note: We can simplify considerably the calculation by using logarithms.

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