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Unit 13: Coefficient of Simple Regression Method

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

)
()( )
()( 5– 21 – 5 5 – 105 – 25 –130
= 2 = = = – 0
545 –
()( ) () 5 225 – 25 200
So the regression equation is
Y – 8 = – 0.65 (X – 6)
Y – 8 = – 0.65 X + 3.9
Y = 11.9 – 0.65 X.
13.2 Coefficients of Simple Regression Method

The quantity b in the regression equation is called the regression coefficient. Since there are two
regression equations there are also two regression coefficients–regression coefficient of X on Y and
regression coefficient of Y on X.

Regression Coefficient of X on Y

b
The regression coefficient of X and Y is represented by the symbol xy or 1 . It measure the change
b
in X corresponding to a unit change in Y. The regression coefficient of X on Y is given by
σ
b xy = r x
σ y
where deviations are taken from means of X and Y, the regression coefficient is obtained by:

Σ xy
b xy * =
Σ y 2

∑ xy ∑ x 2 2
* r = , σ = and σ y = ∑ y
x
∑ 2 × x ∑ y 2 N N
Substituting these values

Σ y 2
Σ xy N Σxy
b xy = × = 2
Σ 2 × x Σ y 2 Σ x 2 Σ y
N

b
where deviations are taken from assumed means, the value of xy is obtained as follows:
N Σ dd y – ( x x )Σ ( d d y ) Σ
b xy = 2
N Σ 2 – ( y d y ) Σ d

Regression Coefficient of Y on X

The regression coefficient of Y on X is represented by b yx or b . It measures the change in Y
2
b
corresponding to unit change in X. The value of yx is given by

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