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The coefficients of the regression βX|y and βY|x, are known, The coefficient of correlation equals: 
1. \(\dfrac{1}{\beta_{X|y}\beta_{Y|x}}\)
2. \(\pm\sqrt{{\beta_{X|y}\beta_{Y|x}}}\)
3. \(\dfrac{2}{\dfrac{1}{\beta_{X|y}}+\dfrac{1}\beta_{Y|x}{}}\)
4. \(\dfrac{\beta_{X|y}+\beta_{Y|x}}{2}\)

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Correct Answer - Option 2 : \(\pm\sqrt{{\beta_{X|y}\beta_{Y|x}}}\)

Explanation

The coefficient of regression is given as = βxIy and βγIx

We know that the coefficient of correlation r = ± √(bxy × byx) where bxy and byx are coefficient of regression

⇒ Similarly from the above options there is only 1 option that satisfied this equation 

∴ The coefficient of correlation is \(\pm\sqrt{{\beta_{X|y}\beta_{Y|x}}}\)

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