Paper 4: Fundamentals of Business Mathematics & Statistic

6.24 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Y Y b (X X)− = yx −

Where YX 2

b = XY

X

∑XY = Sum of product of deviations taken from actual mean of X & Y

∑X^2 = Sum of square of deviations from actual mean of X.

Example 16: From the data of the previous example find the two regression equation by taking deviations

from actual mean.

Soluation:

Table : Calculation Regression Equations

X Y X X x− = Y Y Y− = x^2 Y^2 XY

10 15 -6 -5 36 25 30

12 18 -4 -2 16 4 8

18 21 2 1 4 1 2

22 26 6 6 36 36 36

25 32 9 12 81 144 108

9 8 -7 -12 49 144 84

∑X = 96 ∑Y = 120 0 0 ∑X^2 = 222 ∑Y^2 = 354 ∑XY = 268

X^9616

= 6 =

Y^12020

= 6 =

Regression equation of x on Y

X-X= b (Y-Y)XY

Where XY 2

b = XY

Y

XY

b^268 0.76

= 354 =

putting the value of bYX in the above equation & also put X 16& Y 20= =

X – 16 = 0.76 (Y – 20)

X – 16 = 0.76Y – 15.2

X = 0.76Y – 15.2 + 16

X = 0.76Y + 0.8