UPSC NDA Math Model Paper 10

Here, The two lines of regression are 8x - 10y = 66 and 40x - 18y = 214
⇒ 10y = 8x - 66
⇒byx = 8/10 = 4/5
And,
40x - 18y = 214
⇒ 40x =18y + 214
⇒bxy = 18/40 = 9/20
Now, Coefficient of correlation =r=√bxy×byx
=±√

4

5

×

9

20

=±√

9

25

=±

3

5

bxy>0 and byx>0
So, r=3∕5
Here, variance of x series is 9
⇒ Standard deviation of x series is
σx=√9=3
We know,

σy

σx

=

byx

r

So, σy=

byx

r

×σx
=

4 5

3 5

×3
= 4
Hence, option (2) is correct.