Page 204 - DECO504_STATISTICAL_METHODS_IN_ECONOMICS_ENGLISH

Statistical Methods in Economics

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

()( ) ( )( ) 0 –80
8–10 – –2
b
xy = = = – 0.278
()( ) ( ) 2 288
8 36–0
23 16
b
X = 8 = 2.875, Y = 8 = 2, xy = – 0.278.
Substituting the values in the equation
X – 2.875 = – 0.278 (Y – 2)
X – 2.875 = – 0.278 Y + 0.556
X = 3.431 – 0.278 Y
If Y = 2.5, X is equal to 3.431 + (0.278 × 2.5)
= 3.431 – 0.695 = 2.736.
Regression Equation of Y on X

Y – Y = b yx ( X – X )

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

) (
)
()
()(– 10–– 1 0 – 80
8
= = = – 0.304
(
)
( 833 – – 1 ) 2 264 –1
Y – 2 = – 0.304 (X – 2.875)
Y – 2 = – 0.304 X + 0.874
Y = 2.874 – 0.304 X
X = 5, Y is equal to 2.874 – (0.304 × 5) = 2.874 – 1.52
= 1.354
r = b xy ×b yx = – ( )– 0.278 ( )– 0.304 = – 0.291.

Example 7: Given that the means of X and Y are 65 and 67, their standard deviations are 2.5 and 3.5
respectively, and the coefficient of correlation between them is 0.8.
(i) Write down the two regression lines.
(ii) Obtain the best estimate of X when Y = 70.
(iii) Using the estimated value of X as the given value of X, estimate the corresponding value of Y.
Solution:
(i) Regression Line of Y on X

σ y
Y- Y = σ x ( r ) X- X

y
Y = 67, X = 65, σ = 3.5, σ = 2.5, r = 0.8
x

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