6. If X=2Y+3 and Y=kX+6 are the regression lines of X on Y and Y on X respectively. Show that 0
Answers
Answer:
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
Answer:
Answer:
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