Paper 4: Fundamentals of Business Mathematics & Statistic

6.42 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

(i) write down the two regression lines

(ii) obtain the best estimate of X, when Y = 70.

[Ans. (i) X = 26.81 + 0.57Y, Y = -5.8 + 1.12X, 66.71]

IMPORTANT FORMULA

REGRESSION EQUATIONS

A. WHEN ACTUAL VALUES ARE TAKEN

The regresssion equation of Y on X is expressed as follows:

Yc = a + bX

∑y = Na + b∑X

∑XY = a∑X + b∑X^2

The regression equation of X on Y is expressed as follows:

Xc = a + bY

∑X = Na + b∑Y

∑XY = a∑Y + b∑Y^2

B. WHEN DEVIATIONS ARE TAKEN FROM ACTUAL MEAN

Regresssion equation of an X is given by

X X b (Y Y)− = XY −

XY 2

b xy

= y

Regression equation of an X is given by

Y Y b (X X)− = YX −

Where YX 2

b xy

x

=^

C. WHEN DEVIATIONS ARE TAKEN FROM ASSUMED MEAN

Regression equation of X on Y is given by

X X b (Y Y)− = XY −

Where ( )

X Y X Y

XY 2

(^2) Y Y
b d d d d
d d
N

= −

−

Regression equation of Y on X is given by

Y Y b (X X)− = YX −

Where

( )

YX X Y X Y

2

2 X

X

b d d d d

d d

N

= −

−