Paper 4: Fundamentals of Business Mathematics & Statistic

6.32 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Regression Equation of Y on X :

Y

X

Y Y r (X X)− = σσ −

Y - 6 = 0.9 1.5 10 (X - 40)

Y - 6 = 0.135 (X-40)

Y - 6 = 0.135 X -5.4

Y = 6 + 0.135X - 5.4

Y = 0.6 + 0.135X

Put X = 60 in regression equation of Y on X.

Y = 0.6 + 0.135 (60)

Y = 0.6 + 8.10

Y = 8.7 crore

Example 21 : Given:

Covariance between X and Y = 16

Variance of X = 25

Variance of Y =16

(i) Calculate coefficient of correlation between X and Y

(ii) If arithmetic means of X and Y are 20 and 30 respectively, find regression equation of Y on X.

(iii) Estimate Y when X = 30

Solution:

Given covariance between X and Y = ∑NXY = 16

Variance of X = σx^2 = 25

σx= 25 = 5

Variance of Y = σY^2 = 16

σY= 16 = 4

Applying formula X Y

r XY^16

= N ⋅σ × σ

(^16) 0.8
=5x4=
(ii) given
X = 20
Y = 30