Question

From the following data calculate co-efficient of correlation : X = 0.85 Y and Y = 0.89 X​

Answer 1

The coefficient of correlation is 0.87.

Given: X = 0.85 Y and Y = 0.89 X​

To find: coefficient of correlation

Solution:

The coefficient of correlation is defined as a statistical measure of the strength of a linear relationship between two variables. It tells about the degree to which changes to the value of one variable predict change to the value of another.

The variables we are given in the question are:

X = 0.85 Y and Y = 0.89 X​

Consider,

X = 0.85 Y

Comparing it with standard equation,

$X = a + b_{xy}Y$

we get, $a = 0 , b_{xy} = 0.85$

Consider,

Y = 0.89 X​

Comparing it with standard equation,

$Y = a + b_{yx}X$

we get, $a = 0, b_{yx} = 0.89$

To calculate the coefficient of correlation, we use the formula,

r = $\sqrt{(b_{xy} b_{yx}) }$   where r is coefficient of correlation

r = $\sqrt{(0.89 * 0.85)}$

r = $\sqrt{0.7565}$

r = 0.87

Hence, the coefficient of correlation is 0.87.

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