Page 189 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Unit 12 : Linear Regression Analysis : Introduction and Lines of Regression

Notes
3 0
= 30 + = 30.5 = 18 + = 18.0
6 6

ΝΣdd − ( xy x )Σd ( y ) Σd
b
YX = 2 2
x −d ( Σ N d x )Σ
6268 3 0 1608 1608
×
−
×
= 2 = = = 0.4773
6 × − 563 () 3 3378 − 9 3369
ΝΣdd ( − x )Σd ( y ) Σd
xy
b YX = 2
y 2 −d ( Σ N d y ) Σ

×
×
−
6268 3 0 1608
= 2 = = 2.00
6134 − () 0 804
×
Therefore, the regression of Y on X is :
( YY ) − = YX ( b − X or (Y – 18) = 0.4773 (X – 30.5)
) X
or Y = 18 + 0.4773X – 14.5577
or Y = 0.4773X + 3.4424
and regression of X on Y is :
( − ) XX = YX ( b YY or (X – 30.5) = 2.0 (Y – 18)
) −
or X = 30.5 + 2.0Y – 36.0
or X = 2.0Y – 5.50
Example 4: In the estimation of regression equations of two variables X and Y, the following
results were obtained :
2
2
X = 20, Y = 30, N = 10, ΣX = 6360, ΣY = 9860, ΣXY = 5900
obtain the two equations.
2
2
Solution: Given that : X = 20, Y = 30, N = 10, ΣX = 6360, ΣY = 9860, ΣXY = 5900
∴ ΣX = NX = 10 × 20 = 200; ΣY = 10 × 30 = 300

ΝΣXY ( − )ΣX ( )ΣY
∴ b YX = 2
Σ NX 2 ( − X )Σ

×
10 × − 5900 200 300 59000 − 60000
= 2 =
10 × ( − 6360 )200 63600 − 40000
−1000
= = – 0.042
23600

ΝΣXY ( − )ΣX ( )ΣY
and b XY = 2
Σ NY 2 ( − Y )Σ

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