Paper 4: Fundamentals of Business Mathematics & Statistic

6.20 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

IMPORTANT FORMULAE

KARL PEARSON’S COEFFICIENT OF CORRELATION

A. WHEN DERIVATIONS ARE TAKEN FROM ACTUAL MEAN

x y

r xy

=Nσ σ

∑

2 2

r xy

x x y

= ∑

∑ ∑

B. WHEN DEVIATIONS ARE TAKEN FROM ASSUMED MEAN

( )( )

( ) ( )

y

x y x y

2 2

2 x 2 y

x

d d d d

r N

d d

d N d N

−

=

− −

∑ ∑

∑

∑ ∑ ∑ ∑

RANK CORRELATION

2

2

R 1 6 D

= −N(N 1)−

∑

(^2131322)
2
D (m m ) (m m ) ...^11
R 1 6^1212
N(N 1)

 + − + − + 

 

= − = −

∑

6.2 REGRESSION ANALYSIS

6.2.1. INTRODUCTION

In the last chapter we studied the concept of statistical relationship between two variables such as -

amount of fertilizer used and yield of a crop; price of a product and its supply, level of sales and amount of

advertisement and so on.

The relationship between such variables do indicate the degree and direction of their association, but they

do not answer the question that whether there is any functional (or algebraic) relationship between two

variables? If yes, can it be used to estimate the most likely value of one variable, given the value of other

variable?

“In regression analysis we shall develop an estimating equation i.e., a mathematical formula that relates

the known variables to the unknown variable. (Then, after we have learned the pattern of this relationship,

we can apply correlation analysis to determine the degree to which the variables are related. Correlation

analysis, then, tells us how well the estimating equation actually describes the relationship). The variable

which is used to predict the unknown variables is called the ‘independent’ or ‘explaining’ variable, and

the variable whose value is to be predicted is called the ‘dependent’ or ‘explained’ variable.” Ya-lun

Chou

6.2.2. DISTINCTION BETWEEN CORRELATION AND REGRESSION

By correlation we mean the degree of association or relationship between two or more variables. Correlation

does not predict anything about the cause & effect relationship. Even a high degree of correlation does

not imply necessarily that a cause & effect relationship exists between the two variables.