Paper 4: Fundamentals of Business Mathematics & Statistic

6.4 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Correlation and Regression

Advantages

(1) It is very easy to draw a scatter diagram

(2) It is easily understood and interpreted

(3) Extreme items does not unduly affect the result as such points remain isolated in the diagram

Disadvantages

(1) It does not give precise degree of correlation

(2) It is not amenable to further mathematical treatment

6.1.9. Karl Pearson’s Coefficient of Correlation

The measure of degree of relationship between two variables is called the correlation coefficient. It is

denoted by symbol r. The assumptions that constitute a bivariate linear correlation population model, for

which correlation is to be calculated, includes the following-(ya-lun chou)

1. Both X and Y are random variables. Either variable can be designated as the independent variable,
   and the other variable is the dependent variable.


2. The bivariate population is normal. A bivariate normal population is, among other things, one in
   which both X and Y are normally distributed.


3. The relationship between X and Y is, in a sense, linear. This assumption implies that all the means of Y’s
   associated with X values, fall on a straight line, which is the regression line of Y on X. And all the means
   of X’s associated with Y values, fall on a straight line, which is the regression line of X on Y. Furthermore,
   the population regression lines in the two equations are the same if and only if the relationship between
   Y and X is perfect- that is r= ± 1. Otherwise, with Y dependent, intercepts and slopes will differ from the
   regression equation with X dependent.
   This method is most widely used in practice. It is denoted by symbol V. The formula for computing coefficient
   of correlation can take various alternative forms depending upon the choice of the user.

No correlation; r— 0