Paper 4: Fundamentals of Business Mathematics & Statistic

6.36 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

X^250 25 and Y^30030

= 10 = = 10 =

XY 2

b 10(7900) (250)(300) 0.4

10(10000) (300)

= − =

−

∴ Regression line of X on Y is

X - 25 = 0.4(Y - 30)

X = 0.4 Y - 12 + 25

X = 0.4Y + 13

∴ Regression line of Y on X is

Y - Y = bXY(X-X)

YX 2 2

b N XY X Y

N X ( X)

= −

−

2

1 0(7900) (250)(300) 1.6

10(6500) (250)

= − =

−

∴ Regression line of Y on X is

Y - 30 = 1.6 (X - 25)

Y = 106 X - 40 + 30

Y = 106 X - 10

Now r = b x bXY YX

= 0.4 x1.6

= 0.8

(Since both bYX and bXY are positive)

Example 25 :

Calculate

(i) Two regression coefficients

(ii) Coefficient of correlation

(iii) Two regression equation from the following information:

N =10 ∑X = 350 ∑Y = 310

∑(X - 35)^2 = 162 ∑(Y - 31)^2 = 222

∑(X - 35)(Y - 31) = 92