If 2x – y + 1 = 0 and x – 2y – 1 = 0 be two regression
equations, then which one is the regression of x on y?
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Answer:
The given equation of the lines of regression are
x+2y−5=0.......(i)
and 2x+3y−8=0.....(ii)
Rewriting the equations (i) and (ii), we have
From equation (i)
y=
2
−x
+
2
5
y=−0.5x+2.5 *regression line of y on x)
b
yx
=r
σ
x
σ
y
=−0.5....(iii)
From eqution (ii),
x=
2
−3
y+
2
8
x=−1.5y+4( regression line of x on y)
b
xy
=r
σ
y
σ
x
∴r
2
=b
yx
×b
xy
=(−0.5)×(−1.5)=0.75
∴ r=
0.75
=±0.866
But b
xy
and b
yx
being both −ve therefore, r is also −ve.
Correlation coefficient (r)=−0.866
Varianceof x i.e., σ
x
2
=12
∴ σ
x
=
12
From equation (iii)
r
σ
x
σ
y
=−0.5
−0.866.
12
σ
x
=−0.5
σ
y
=
0.866
0.5×
12
=2
∴ Variance of y i.e., σ
y
2
=4
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