Page 203 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 13: Coefficient of Simple Regression Method

Regression Coefficient of X on Y Notes

N Σ dd y – Σ d Σ x d y
x
b xy = 2
N Σ d 2 – Σ ( y y ) d

2
Σ dd x = + 3, dΣ y = 2, dΣ y = 372, N = 7
x y = – 132, dΣ
) ( )( )
()(–132 – 3 2 – 924–6
7
b xy = = = – 0.353
) ( )
()(372–2 2 2,604 – 4
7
Regression Coefficient of Y on X
N Σ dd – Σ d Σ d
b yx = x y x y
N Σ d 2 ( x d x ) – Σ 2

) ( )( )
7
()(–132 – 3 2 – 924–6
= = = – 2.473.
755 –
()( ) ( ) 3 2 385–9
Example 6: Given the bivariate data:
X 1 5 3 2 1 1 7 3
Y 6 1 0 0 1 2 1 3

(a) Fit a regression line of Y on X and thence predict Y if X = 5.
(b) Fit the regression line of X on Y and thence predict X if Y = 2.5.
Solution:
X (X – 3) Y (Y – 2)

d x d x 2 d y d y 2
1 – 2 4 6 + 4 16
5 + 2 4 1 – 1 1
3 0 0 0 – 2 4
2 – 1 1 0 – 2 4
1 – 2 4 1 – 1 1
1 – 2 4 2 0 0
7 + 4 16 1 – 1 1
3 0 0 5 + 3 9
2
2
Σ X = 23 Σ d x = – 1 ∑ d x = 33 Σ Y = 16 Σ d y = 0 Σ d y = 36
Regression Equation of X on Y

b
X – X = xy ( Y – Y )

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