NIMCET 2011 — Mathematics PYQ

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Question

NIMCET 2011 — Mathematics PYQ

NIMCET | Mathematics | 2011

Two variables have least square regression lines $3x + 2y = 26$ and $6x + y = 31$ , then correlation between $x$ and $y$ is:

Choose the correct answer:

Explanation

Solution:

1. Find Regession Coefficients ( $b_{yx}$ and $b_{xy}$ ):

Let $3x + 2y = 26$ be the line of $y$ on $x$ :

2y = -3x + 26 \Rightarrow y = -\frac{3}{2}x + 13

b_{yx} = -1.5

Let $6x + y = 31$ be the line of $x$ on $y$ :

6x = -y + 31 \Rightarrow x = -\frac{1}{6}y + \frac{31}{6}

b_{xy} = -\frac{1}{6}

2. Calculate Correlation Coefficient ( $r$ ):

r = \pm \sqrt{b_{yx} \cdot b_{xy}}

r = \pm \sqrt{(-1.5) \cdot \left(-\frac{1}{6}\right)} = \pm \sqrt{\frac{1.5}{6}} = \pm \sqrt{0.25} = \pm 0.5

3. Determine Sign:

Since both $b_{yx}$ and $b_{xy}$ are negative, $r$ must be negative.

r = -0.5

The correct option is (d) -0.5.

Choose the correct answer:

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