Question

What would be the Value of X if y is 20 and regression equation of Y on X: y=5+0.5X

Answer 1

Step-by-step explanation:

Question

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The regression equation of Y on X is y=

9

2

x and the regression equation of X on Y is x=

2

y

+

6

7

Find: a. Correlation coefficient between X and Y.

b. σ

y

2

if σ

x

2

=4.

Medium

Solution

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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