Question

21. If xy = 2800, X = 16, y = 16, n = 10, variance of x is 36 and variance of y is 25
then correlation coefficient r(x, y) is equal to
(2)
(A) 0.95
(B) 0.73
(C) 0.8
(D) 0.65​

Answer 1

Answer:

correlation coefficient r(x, y) is equal to 0.95

Step-by-step explanation:

Given :

Cov (x,y)  = 2800

V(x) =36

V(y) = 25

As we know formula of correlation coefficient  is :

Let r be Correlation coefficient of x,y

Then

r = $\frac{Covarience(x,y)}{\sqrt{V(x)*V(y)} }$

on solving

⇒$\frac{2800}{\sqrt 36*25}$

⇒$\frac{2800}{\sqrt 900}$

⇒$\frac{2800}{30}$

⇒0.95

correlation coefficient r(x, y) is equal to 0.95

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Answer 2

Answer:

The correct answer is option(A).

The value of Correlation coefficient r(x, y) is 0.95

Explanation:

The given values in the question are:

xy = 2800, X = 16, y = 16, n = 10,

variance of x is 36 and

variance of y is 25

We need to compute correlation coefficient r(x, y).

Formula for computing correlation coefficient is:

correlation coefficient = Cov(x, y) / √V(x) X V(y)

Put all values in the above formula

We get,

= 2800/√36 X 25

= 2800/6 X 5

= 2800/30

= 0.95

Hence, 0.95 option (A) is the correct answer.

Additional Knowledge:

• The correlation coefficient is a statistical measure. It is used to find the strength of the relationship between the relative movements of two variables.
• It also shows how one variable moves in relation to another.
• A positive correlation indicates that the both of the variables move in the same direction.
• While a negative correlation coefficient indicates that they move in opposite directions.
• And a correlation of zero indicates no correlation at all.

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