Paper 4: Fundamentals of Business Mathematics & Statistic

6.30 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Solution: Let the marks in Maths be denoted by X and the marks in English by Y.

We have: X = 40

Y = 50

σX= l0

σY= l6

r = 0.5

Regression Equation of Y on X

Y - Y r (X X)YX

= σ −

σ

Regression Equation of X on Y

X

Y

X X r (Y Y)− = σσ −

Regression Equation of Y on X

Y

X

Y Y r (X X)− = σσ −

Y - 50 = 0.5^1610 (X - 40)

Y - 50 = 0.8 (X - 40)

Y - 50 = 0.8X - 32

Y - 50 = 0.8X - 32

Y = 18 + 0.8X

Regression Equation of X on Y

X

Y

X X r (Y Y)− = σσ −

X - 40 = 0.5^1016 (Y - 50)

X - 40 = 0.3125 (Y - 50)

X = 40 + 0.3125Y -15.625

X = 24.375 + 0.3125Y

To find likely marks in Maths if marks in English are 40, put Y = 40 in regression equation of X on Y.

X = 0.3125 (40) + 24.375

= 12.5 + 24.375

= 36.875