Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.35

Regression Equation of Y on X

Y

X

Y Y r (X X)− = σσ −

Y - 35 = 0.8 107 (X - 30)

Y - 35 = 0.56 (X- 30)

Y - 35 = 0.56X - 16.8

Y = 0.56X - 16.8 + 35

Y = 0.56X + 18.2

Regression Equation of X on Y

X

Y

X X r (Y Y)− = σσ −

X 30 0.8 (Y 35)^10

− = 7 −

X - 30 = 1.14 (Y - 35)
X - 30 = 1.14Y - 39.9
X = 1.14Y - 39.9 + 30

X = 1.14Y - 9.9
To find likely marks in accounts if marks in statistics are 40, put Y = 40 in regression equation of X on Y.

X = 1.14 (40) -9.9
X = 45.6 - 9.9
= 35.7
Marks in accounts = 35.7
Example 24 :
By using the following data, find out the two lines of regression and from them compute the Karl Pearson’s
coefficient of correlation.
∑X = 250, ∑Y = 300, ∑XY = 7900, ∑X^2 = 6500, ∑Y^2 = 10000, N = 10

Solution: Regression line of X on Y is :

X - X = bXY(Y-Y)

Where,

XY 2 2

b N XY X Y, X X and Y Y

N Y ( Y) N N

= − = =

−