Question

Given that Sigma X: 120, Sigma Y: 432, Sigma XY: 4992, Sigma X square: 1392, Sigma Y square: 18252 N: 12 Find out 1. The two regression coefficients, 2. The two regression equations.​

Answer 1

Answer:

Answer

The repression equation of y on x is y=

9

2

x

Comparing with y−

y

ˉ

=b

yx

(x−

x

ˉ

)

Here, b

yx

=

9

2

Now, the regression equation of x on y is x=

2

y

+

6

7

Comparing with x−

x

ˉ

=b

xy

(y−

y

ˉ

)

Here, b

xy

=

2

1

Part (a)

We have, correlation coefficient between x and y is

r=

b

yx

.b

xy

r=

9

2

×

2

1

r=±

3

1

Therefore,

r=

3

1

(Since b

yx

and b

xy

are positive)

Part (b)

Since, σ

x

2

=4⇒σ

x

=2

We have,

b

yx

=r.

σ

x

σ

y

Therefore,

9

2

=

3

1

.

2

σ

y

σ

y

=

3

4

Hence, this is the answer.