Question

How to find the mean of x and y when two equation is given

Answer 1

Q)  

Two lines of regression are given by x+2y-5=0, 2x+3y-8=0 and σ2x("sigma squared"x)=12, Calculate the mean value of x and y, variable of Y and the coefficient of correlation between x and y.

Step-by-step explanation:

A)  

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