Page 160 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

Notes The only difference is that of the symbols. Since in this question we were given
series X and X we changed the symbols in the formula accordingly.
1
2
Calculation of Correlation Coefficient when Change of Scale and Origin is
made
Since r is a pure number, shifting the origin and changing the scale of series do not affect its value.
Example 5: Find the coefficient of correlation from the following data:

X : 300 350 400 450 500 550 600 650 700

Y : 800 900 1000 1200 1300 1400 1500 1600
Solution: In order to simplify calculations, let us divide each value of the variable X by 50 and
each value of variable Y by 100.
CALCULATION OF CORRELATION COEFFICIENT

X Y
X ( X– X 1 ) x 2 Y ( Y– Y 1 ) 1 y 2 xy
1
50 100
X 1 X = 10 Y 1 Y = 12
1
1
x y
300 6 – 4 16 800 8 – 4 16 16
350 7 – 3 9 900 9 – 3 9 9
400 8 – 2 4 1,000 10 – 2 4 4
450 9 – 1 1 1,100 11 – 1 1 1
500 10 0 0 1,200 12 0 0 0
550 11 + 1 1 1,300 13 + 1 1 1
600 12 + 2 4 1,400 14 + 2 4 4
650 13 + 3 9 1,500 15 + 3 9 9
700 14 + 4 16 1,600 16 + 4 16 16
2
∑X = 90 ∑x = 0 ∑x 2 = 60 ∑Y = 108 ∑y = 0 ∑y = 60 ∑xy = 60
1
1
∑xy
r =
∑ 2 ×x ∑ y 2

2
2
∑xy = 60, ∑x = 60, ∑y = 60
60 60
r = = = 1.
60 × 60 60
When Deviations are taken from an Assumed Mean

When actual means are in fractions, say the actual means of X and Y series are 20.167 and 29.23, the
calculation of correlation by the method discussed above would involve too many calculations and
would take a lot of time. In such cases we make use of the assumed mean method for finding out
correlation. When deviations are taken from an assumed mean the following formula is applicable:

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