Paper 4: Fundamentals of Business Mathematics & Statistic

6.26 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Solution: Table : Calculation Regression Equations

X Y dx dy dx^2 dy^2 dxdy

10 12 -5 -13 25 169 65

12 15 -3 -10 9 100 30

15 25 0 0 0 0 0

19 35 4 10 16 100 40

15 14 0 -11 0 121 0

∑X =71 ∑Y= 101 ∑dX= -4 ∑dY=-24 ∑dX^2 = 50 ∑d^2 Y= 490 ∑dXdY=135

X^71 14.2

= 5 =

Y^101 20.2

= 5 =

Since X& Y are not an integer we would solve it by taking assume mean of 15 from X series, and 25 from Y

series

REGRESSION EQUATION OF X ON Y

X X b (Y Y)− = XY −

( )

XY X Y X 2 Y

2 Y

Y

b d d d d

d

d N

=^ −

By putting the values from the above table we get

XY ( ) 2

b 135 ( 4)x( 24)

490 24

5

= − − −

− −

135 96

490 576

5

= −

−

(^3939) 0.104
=490 115.2 374.8− = =
X X b (Y Y)− = XY −
X – 14.2= 0.104 (Y – 20.2)
X – 14.2 = 0.104Y – 2.10
X = 0.104Y – 2.10 + 14.2
X = 0.104Y + 12.1
Regression equation of Yand X