Question

If the two regression coefficients are byx = 3 and bxy = 1/3, the correlation coefficient is ​

Answer 1

SOLUTION

GIVEN

Two regression coefficients are

$\displaystyle \sf{b_{yx} = 3 \: \: \: \: and \: \: \: b_{xy} = \frac{1}{3} }$

TO DETERMINE

The correlation coefficient

CONCEPT TO BE IMPLEMENTED

If among the two variables x and y in a bivariate distribution, y is taken as dependent variable and x as independent variable then the corresponding regression curve like y = f(x) is known as regression curve of y on x

From this curve we may get approximately the value of the variable y by knowing the variable x

EVALUATION

Here it is given that

The regression coefficient of x on y

$\displaystyle \sf{ b_{xy} = \frac{1}{3} }$

Regression coefficient of y on x

$\displaystyle \sf{b_{yx} = 3 \: }$

Since both regression coefficient is positive

So the correlation coefficient is also positive

So the correlation coefficient is

$\displaystyle \sf{r_{xy} = + \sqrt{b_{xy} \: \times \: b_{yx} }}$

$\displaystyle \sf{ \implies \: r_{xy} = + \sqrt{ \frac{1}{3} \times 3 }}$

$\displaystyle \sf{ \implies \: r_{xy} = 1}$

Hence the required correlation coefficient = 1

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