Question

Two variables $x$and $y$are related by the linear equation $ax+by+c=0$ The coefficient of correlation between the two is $+1,$ if

• A. $a$ is positive
• B. $b$ is positive
• C. $a$ and$b$ both are positive
• D. $a$ and $b$ are of opposite sign

Answer 1

The correct option is D

$a$ and $b$ are of opposite sign

Solve the relation between $a$ and $b$ :

The given relation is $ax+by+c=0.$

$by=–ax–c$

$y=\left(-\frac{a}{b}\right)x-\left(\frac{c}{b}\right)$

Since $⍴=1,$if the slope of relation is positive.

$a$ and $b$are of opposite signs.

Hence, option (D) is the correct answer.