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Question: The two lines of regression are given by \(3x + 2y = 26\) and\(6x + y = 31\). The coefficient of cor...

The two lines of regression are given by 3x+2y=263x + 2y = 26 and6x+y=316x + y = 31. The coefficient of correlation between x and y is

A

−13- \frac{1}{3}

B

13\frac{1}{3}

C

−12- \frac{1}{2}

D

12\frac{1}{2}

Answer

−12- \frac{1}{2}

Explanation

Solution

Here, 3x+2y=26⇒y=−32x+133x + 2y = 26 \Rightarrow y = - \frac{3}{2}x + 13

and 6x+y=31⇒x=−16y+3166x + y = 31 \Rightarrow x = - \frac{1}{6}y + \frac{31}{6}

∴\therefore r=(−32)(−16)=−12r = \sqrt{\left( \frac{- 3}{2} \right)\left( - \frac{1}{6} \right)} = - \frac{1}{2}.