coefficient of correlation of 10 pairs of observations is 0.8. if all the observations are multipled by 2, coefficient of correlation for new set of data will be
Answers
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
Hard
Solution
verified
Verified by Toppr
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
Answer:
The following data are provided for 10 pairs of observations on two variables x and y.
∑(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
Hard
Solution
verified
Verified by Toppr
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, the 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