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Regression

Theory and Formula


Question


Q1. ∑ x = 50, ∑ y = 80 , ∑ xy = 500, x = 10 . Find the cov(x + 10, y + +16)

(a) 10

(b) 3

(c) 4

(d) 2

Solution. a
Cov(x,y) =
1/x
∑xy - x̅ y̅

=
1/10
x 500 -5 x 8

= 50 - 40 = 10
Solution

Q2. The regression equations of y on x is 4x - 5y + 33 = 0 , if variance of x is 25,
then cov(x,y) is

(a) 4

(b) 5

(c) 6

(d) 20

Solution. d
4x - 5y = -33

-5y = -4x - 33

y =
4/5
x +
33/5


bxy =
4/5


S.D of x = 5

bxy =
cov(x,y)/σx2


4/5
=
cov(x,y)/25


cov(x,y) = 20
Solution

Q3. Coefficient non-determination is 0.64 , S.D of x is 4.8 and S.D of y = 9.6 , find regression coefficient x on y .

(a) 0.3

(b) 0.4

(c) 0.5

(d) 0.6

Solution.a
bxy = r
σx/σy2


= 0.6 x
4.8/9.6
= 0.3
Solution

Q4. bxy = -3.2 , coefficient of determination is 0.80 , line y on x is Bx + y + 12 = 0 , the value of B is .

(a) -0.25

(b) 0.19

(c) 0.48

(d) None

Solution.
Line y on x

y = -Bx - 12

r2 = byx . bxy

0.80 = byx (3.2)

byx =
0.80/3.2
= 0.25

byx = - 0.25 (∴ bxy is negative)
Solution

Q5. If ∑ (x - x̅) (y - y̅) = -20 , coefficient of determination is 0.81 then

(a) Curve will constant

(b) Curve move upper left to lower right

(c) Curve move upper left to lower right

(d) can't say

Solution. b
Note : If ∑ (x - x̅) (y - y̅) is negative then covariance will negative, if cov(x,y) < 0 then r will negative .
Solution