Paper 4: Fundamentals of Business Mathematics & Statistic

6.16 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Example12 :

From the following data, calculate Karl Pearson’s coefficient of correlation

Height of fathers 66 68 69 72 65 59 62 67 61 71

(in inches)

Height of sons 65 64 67 69 64 60 59 68 60 64

(in inches)

Solution: Table Calculation of coefficient of correlation between height of fathers and height of sons

X Y x y x^2 y^2 xy

1 66 65 0 1 0 1 0

2 68 64 2 0 4 0 0

3 69 67 3 3 9 9 9

4 72 69 6 5 36 25 30

5 65 64 -1 0 1 0 0

6 59 60 -7 -4 49 16 28

7 62 59 -4 -5 16 25 20

8 67 68 1 4 1 16 4

9 61 60 -5 -4 25 16 20

10 71 64 5 0 25 0 0

∑X 660= ∑Y 640= ∑x 166^2 = ∑y 108^2 = ∑xy 111=

X X

= N

∑

(^660) 66inches
= 10 =
Y Y
= N
∑
(^640) 64inches
= 10 =
2 2
r Xy
x y
= ∑
∑ ∑
r^111
166x108

=

= 0.829