Question

Find number of pairs of observations from the following data.


= - 0.4, Ex = 100, Ex2 = 2250, Ey = 100, Ey = 2250, Exy = 1900.

Answer 1

Answer:

11th

Economics

Correlation

Correlation Coefficient

For 10 pairs of observation...

STATISTICS

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Asked on October 15, 2019 by

Yoga Baghla

For 10 pairs of observation on two variables x and y, the following data are available.

∑(x−2)=30,∑(y−5)=40,∑(x−2)

2

=900.

∑(y−5)

2

=800,∑(x−2)(y−5)=480.

Find the correlation coefficient between x and y

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VIDEO EXPLANATION

ANSWER

Let x=x

i

and y=y

i

Let u

i

=x

i

−2 and v

i

=y

i

−5

Then it is given that,

n=10,∑u

i

=30,∑v

i

=40,∑u

i

2

=900,∑v

i

2

=800,∑u

i

v

i

=480

∴

u

=

n

∑u

i

=

10

30

=3

v

=

n

∑vi

=

10

40

=4

Since the correlation coefficient is independent of change of origin and scale, correlation coefficient between x and y is

r(x,y)=r(u,v)

=

n

1

∑u

i

2

−(

u

)

2

⋅

n

1

∑v

i

2

−(

v

2

)

n

1

∑u

i

v

i

−

u

v

=

10

900

−(3)

2

⋅

10

800

−(4)

2

10

480

−3×4

=

81

⋅

64

48−12

=

9×8

36

=

8

4

=0.5