Paper 4: Fundamentals of Business Mathematics & Statistic

6.12 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Example 7 :

Find the coefficient of correlation from the following data and interpret your result

Prices (X) 300 350 400 450 500 550 600 650 700

Sales (Y) 800 900 1000 1100 1200 1300 1400 1500 1600

Solution:

Table : Calculation of correlation coefficient

X Y x=X X 50 − y=Y Y 100 − x^2 y^2 xy

300 800 -4 -4 16 16 16

350 900 -3 -3 9 9 9

400 1000 -2 -2 4 4 4

450 1100 -1 -1 1 1 1

500 1200 0 0 0 0 0

550 1300 1 1 1 1 1

600 1400 2 2 4 4 4

650 1500 3 3 9 9 9

700 1600 4 4 16 16 16

∑X 4500= ∑Y 10800= ∑X 0= ∑y 0= ∑X 60^2 = ∑X 60^2 = xy 60=

Note that as r is a pure number, change of scale does not affect its value. Hence the values are divided by

50 in column 3 and are divided by 100 in column 4 to make the calculations simple.

X X^4500500

= N 9= =

Y Y^108001200

= N 9= =

∑

2 2

r xy

x y

=

⋅

60

60 60

=

×

60

= 60 = 1

Since r = +1, there is perfect positive correlation between X and Y.