the equation of regression line of y on x is 5y +3x= 5 and the equation of regression line of x on y 3y + 5x+ 2=0 find the correlation coefficient between x and y.
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The two regression lines are
3x−2y=5....(1)
x−4y=7....(2)
From equation (1) 3x−2y=5
3x=2y+5
x=
3
2
y+
3
5
∴b
xy
=
3
2
(Regression of x on y)
From equation (2) x−4y=7
4y=x−7
y=
4
x
−
4
7
∴b
yx
=
4
1
(Regression of y and x)
The two regression lines are
Coefficient of correlation =∣r∣
=
b
xy
⋅b
yx
=
4
1
×
3
2
=
6
1
=
6
6
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