Correlation
Question
Q1.
If bxy is zero, find rxy
(a) 0 (b) 1 (c) 2 (d) -1
Solution.
r = √(bxy . byx), so if bxy = 0
then rxy = 0
Solution
Q2.
Cov(x,y)< 0 , means
(a) Negative correlation (b) Positive correlation (c) Non correlation
(d) None of these
Cov(x,y)/σx . σy
σx and σy can not be negative , so if Cov(x,y)is negative then r will negative .
Solution
Q3.
When rxy = ± 1 , then the regression lines
(a) Perpendicular to each other (b) Coincide
(c) Parallel to each other (d) None of these
Solution.
(b) Coincide
Solution
Q4.
The value of Rxy of a certain number of observations was found to be
2/3
. The sum of the squares of differences between the
corresponding rank was 55, find the number of pairs .
Solution.
R = 1 -
6 ∑d2/x(x2 - 1)
2/3
= 1 -
6 x 55/x(x2 - 1)
⇒ n = 10
Solution
Q5.
The intersection of both the regression lines give us
(a) mean of x & y (b) mode of x & y
(c) S.D of x & y (d) None
Solution.
(a) mean of x & y
Solution
Q6.
If ∑x = 50 , ∑y = 80 and ∑ xy = 400 , find r .
Solution.
r =
cov(x,y)/(S.D of x) . (S.D of y)
cov(x,y) =
1/x
∑ xy - x̄ȳ =
1/10
x 400 - 40 = 0
So, r = 0
Solution
Q7.
Line 2x - 3y = 0 is line y on x , find byx .
Solution.
2x - 3y = 0
- 3y = - 2x ⇒ y =
2/3
x
b
yx =
2/3
Note : for line y on x
y = a + bx
where b = regression coefficient y on x (b
yx)
Solution
Q8.
If scatter diagram of two variables shows movement from lower left two upper right then it shows __________ correlation .
Solution.
Positive
Solution
Q9.
If r holds negative sign then bxy holds ___________ sign .
Solution.
Negative sign .
Note : All the three coefficient have same sign (two regression coefficients and correlation coeffi
cient).
Solution
Q10.
The geometric mean of both regression coefficient gives us ______________
Solution.
correlation coefficient
Solution
