Paper 4: Fundamentals of Business Mathematics & Statistic

6.8 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Since mean of X and Y are in decimals i.e. 11.5 and 12.1 respectively hence we would solve by method II

( )( )

( ) ( )

d dx y

d d -x y

r = N

2 2

2 d 2x dy

d -x d -y

N N

Taking Ax as 10 and Ay as 15

( )

( ) ( )

108 1 5 29

10

152 292

(^2351030710)
64 5
212 5 222 9
64 5 64 5
47366 25 217 63

− − × −

=

− − −

= −

×

= − = −

.

..

..

..

r

r

= – 0.296

Example 3:

Find correlation between age of husband and age of wife.

Age of Husband (X) 46 54 56 56 58 60 62

Age of Wife (Y) 36 40 44 54 42 58 54

Solution:

Table : Calculation of correlation coefficient

X Y dx = x-Ax dy = y-Ay d^2 x d^2 y dxdy

46 36 -10 -9 100 81 90

54 40 -2 -5 4 25 10

56 44 0 -1 0 1 0

56 54 0 9 0 81 0

58 42 2 -3 4 9 -6

60 58 4 13 16 169 52

62 54 6 9 36 81 54

SX=392 SY=328 Sdx = 0 Sdy = 13 Sd^2 x =160 Sd^2 y=447 Sdxdy=200

Since mean of Y is in decimals i.e. 46.85, we would solve it by short cut method

( )( )

( ) ( )

d dx y

d dx y N

r 2

d^2 d

d^2 x d^2 y

x N y N

−

=

− −