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Statistical Methods in Economics

Notes Regression Equation of Y on X

Y – Y = ( X – Xb yx )

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

Once the value of b and b are determined in the above manner the regression equations can be
xy
yx
obtained very easily.
Example 3: From the data of Example 1, obtain regression equations taking deviations from 5 in case
of X and 7 in case of Y.
Solution:

X (X – 5) Y (Y – 7)
d d 2 d d 2 d d
x x y y x y
6 + 1 1 9 + 2 4 + 2
2 – 3 9 11 + 4 16 – 12
10 + 5 25 5 – 2 4 – 10
4 – 1 1 8 + 1 1 – 1
8 + 3 9 7 0 0 0
2
∑ X = 30 ∑ d = + 5 ∑d x 2 = 45 ∑ Y = 40 ∑ d = 5 ∑ d y = 25 ∑dd = – 21
xy
y
x
Regression Equation of X on Y
b
X – X = xy ( Y – Y )

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

)
()( )
()( 5– 21 – 5 5 –105 – 25
= 2 = = – 1.3
()( ) () 5 125 – 25
525 –
30 40
X = 5 = 6, Y = 5 = 8
Hence the regression equation is
X – 6 = – 1.3 Y (– 8)
X – 6 = – 1.3 Y + 10.4
or X = 16.4 – 1.3 Y
Regression Equation of Y on X
b
Y – Y = yx ( ) X – X

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