If x + 2y = 5 and 2x + 3y = 8 are 2 regression lines then regression line y on x is
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Step-by-step explanation:
Solution :
x+2y=5
2x+3y=8
and σ2x=12
On solving the two equations, we can obtain the mean values for x and y
x+2y=5
2x+4y=10
2x+3y=8
______________
0+y=2
y=2
and x=1
a) Hence the mean value for x and y is 1 and 2
x+2y=5
x=5−2y
bxy=−2
2x+3y=8
3y=8−2x
y=83−−23x
∴byx=−23
b) Coefficient of correlation 'r' is byx,bxy−−−−−−√
r=−2×−23−−−−−−−−√
=43−−√
c) byx=r.σyσx
but σ2x=12
=> σx=12−−√
σy=byx×σxr
=−23×12−−√43−−√
=−23×23–√×3–√2
=−2
σy=−2
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