Paper 4: Fundamentals of Business Mathematics & Statistic

6.22 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Solution : Table : Calculation of Regression Equations

X y x^2 Y^2 XY

10 15 100 225 150

12 18 144 324 216

18 21 324 441 378

22 26 484 676 572

25 32 625 1024 800

9 8 81 64 72

∑X = 96 ∑Y = 120 ∑X^2 = 1758 ∑Y^2 = 2754 ∑XY = 2188

Regression equation of X on Y is given by :

X = a + bY

Where a & b can be found out by solving the following 2 equations simultaneously –

∑X = Na + b ∑Y

∑XY = a∑Y + b∑Y^2

Substituting the values obtained from the table above, we get

96 = 6a + 120 b ....(1)

2188 = 120a + 2754b ....(2)

Multiply equation 1 by 20 & subtract equation 2 from it.

1920 = 120a + 2400 b

-^2188 = -120a - 2754 b- -

• 268 = 0 - 354 b

b = −−^268354

b = 0.76

Put this value of b in eq ........ (1)

96 = 6a + 120 x 0.76

96 = 6a + 91.2

6a = 96 – 91.2

a 4.8 0.8

= 6 =

Put the value a & b in the regression equation of X on Y

X = a + by

X = 0.8 + 0.76Y