Q1.
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
Q2.
In rank correlation method , if ∑ d2 = 0 , find the value of rank correlation coefficient (R) .
R = 1 -
6 ∑ d2/n(n2 - 1)
if ∑ d
2 = 0 ⇒ R = 1(Perfectly positively correlation).
Q3.
If ∑x = 50 , ∑y = 80 and ∑ xy = 400 , n =10 find r .
Solution.
r =
cov(x,y)/(S.D of x) . (S.D of y)
cov(x,y) =
1/n
∑ xy - x̄ȳ =
1/10
x 400 - 40 = 0
So, r = 0
Solution
Q4.
rxy = 0.83 , find the value of ruv if u = x - 10 and v = y + 12 .
Solution.
ruv = 0.83
Note: change of origin has no impact on correlation coefficient .
Solution
Q5.
If rxy = 0.92 , find ruv if
u =
x - 20/19
and
v = y - 33/(- 23)
Solution.
ruv = -0.92
Note : If change of scale has different sign the r will reverse .
Solution
Q6.
If the angle betweeen the two regression line increases , then correlation between the variables .
(a) Decreases (b) Increases (c) Remain same (d) Can't say
Solution.
(a) Decreases
Solution
Q7.
In the regression line y = a + bx , a is know as
(a) Intercept of line (b) Slop of the line (c) Can't say
(d) None
Solution.
(a) Intercept of line
Solution
Q8.
The sign of regression coefficient and correlation coefficient are always
(a) same (b) opposite (c)reciprocal to each
other (d) can't say
Solution.
(a) same
Solution
Q9.
If two variables are linearly independent then the value of two regression coefficients is _________________ .
Solution.
zero
Solution
Q10.
The regression line y on x can be written as .
Solution.
y - ȳ = byx (x - x̄)
Solution
