Aspire Faculty ID #16170 · Topic: NIMCET 2011 · Just now
NIMCET 2011

Regression lines: $3x+2y=26$, $6x+y=31$ Correlation between $x,y$ is

Solution

Slope of line of $y$ on $x$: 
$3x+2y=26 \Rightarrow y=-\dfrac{3}{2}x+13$ 
Slope of line of $x$ on $y$: 
$6x+y=31 \Rightarrow x=-\dfrac{1}{6}y+\dfrac{31}{6}$ 

 Product of slopes $=r^{2}$ with sign of slopes: 
$r=\sqrt{(-3/2)\cdot(-1/6)}$
$=\sqrt{1/4}$
$=1/2$
Both slopes negative ⇒ $r$ negative.
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