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Unit 13: Coefficient of Simple Regression Method

Notes
σ
b xy ,= r σ x y

0.6 × 4
0.8 =
σ y

2.4
σ y = 0.8 = 3.

Example 4: Obtain the value of the correlation coefficient through the method of regression analysis
from the data given below first by taking deviation from the actual means of X and Y and secondly
from assumed means 2 and 18 for series X and Y respectively.

X 1 2 3 4 5
Y 10 20 15 25 30

Solution:
(a) Calculation of Regression Coefficient from the actual means

X (X – 3) Y (Y – 20)
x x 2 y y 2 xy

1 – 2 4 10 – 10 100 20
2 – 1 1 20 0 0 0
3 0 0 15 – 5 25 0
4 + 1 1 25 + 5 25 5
5 + 2 4 30 + 10 100 20

2
2
Σ X = 15 Σ x = 0 Σ x = 10 Σ Y = 100 Σ y = 0 Σ y = 250 Σ xy = 45
15 100
X = 5 = 3, Y = 5 = 20

Regression Coefficient of X on Y

Σxy 45
b xy = Σ y 2 = 250 = 0.18

Regression Coefficient of Y on X

Σ xy 45
b yx = 2 = = 4.5
Σ x 10

r = b xy ×b yx = 0.18 × 4.5 = 0.81 = 0.9.

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