Math, asked by sarkarsneha038, 7 months ago

If 2x – y + 1 = 0 and x – 2y – 1 = 0 be two regression
equations, then which one is the regression of x on y?​

Answers

Answered by mauryasuresh841
0

Answer:

The 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

Varianceof x i.e., σ

x

2

=12

∴ σ

x

=

12

From equation (iii)

r

σ

x

σ

y

=−0.5

−0.866.

12

σ

x

=−0.5

σ

y

=

0.866

0.5×

12

=2

∴ Variance of y i.e., σ

y

2

=4

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