If the two regression lines are 3x + y = 46 and 3y + 12x = 19, find which one among them is the regression line of x on y and which one is the regression line of y on x, justify your answer If the variance of x is 4, find the means, the correlation coefficient and the variance of y.
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Given lines of regression are:
3x+12y−19=0 .........(1)
9x+3y−46=0 ..........(2)
From equation (1), the regression line of y on x is.
12y=−3x+19
⇒y=−
12
3
x+
12
19
⇒y=−
4
1
x+
12
19
∴b
yx
=−
4
1
From equation (2), the regression line of x on y is.
9x=−3y+46
⇒x=−
9
3
y+
9
46
⇒x=−
3
1
y+
9
46
∴b
xy
=−
3
1
Now, r=
b
yx
⋅b
xy
r=
(−
4
1
)×(−
3
1
)
r=
12
1
r=0.288.
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