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Question

The regression of savings (s) of a family on income ymay be expressed as s=a+ym, where a and m are constants. In a random sample of 100 families, the variance of savings is one-quarter of the variance of incomes and the correlation is found to be 0.4 the value of m is


A

2

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B

5

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C

8

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D

None of these

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Solution

The correct option is B

5


Explanation for the correct answer:

Finding the value of m:

Given that, s=a+ym,s2=14y2 and r=0.4

s=a+ymands=a+ym

On subtracting s-s, we get

s-s=1my-y...(i)s-sy-y=1my-y2

Also, Cov(s,y)=1my2...(ii)

Finding the value of m.

r=cov(s,y)sy0.4=1my2sy0.4=1mys0.2=1mm=5

Therefore, the correct answer is option (B).


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