NIMCET 2011 Question Paper with solutions

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Question : 33 of 120

Marks: +1, -0

Two variables have least square regression lines

3 x+2 y=26

and

6x+y=31

, then correlation between

x

and

y

is

0.5
0.7
-0.7
-0.5

Solution:

Let line of regression y on

x

is

y=- {3}/{2} x+13

and

x

on

y

is

x=- {y}/{6}+{31}/{6}

b_{y x}=- {3}/{2}

and

b_{x y}=- {1}/{6}

∴ r=-√{b_{y x} ⋅ b_{x y}}

=-√{(- {3}/{2})(- {1}/{6})}=-√{ {1}/{4}}

=-\;{1}/{2}=-0.5

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