Unit 6 : STATISTICS AND INFERENCE
Unit 6.1 Correlation and Regression
Properties of Correlation Coefficient
The properties of ‘r’ are as follows:
a. ‘r’ has no unit. It is a pure number. It means units of measurement are not parts of ‘r’.
b. A negative value of ‘r’ indicates an inverse relation, and if ‘r’ is positive then the two variables
move in the same direction.
c. If r=0,the two variables are uncorrelated. There is no linear relation between them. However ,
other type of relation may be there !
d. If r =1 or r= -1, the correlation is perfect or proportionate. A high value of ‘r’ indicates strong
linear relationship i.e., +1 or -1.
e. The value of the correlation coefficient lies between -1 and +1. i.e.,
If the value of ‘r’ lies outside the range, it indicates error in calculation !
f. It is independent of change of origin and scale, which means the coefficient of correlation remains
invariant under a change of origin and change of scale.
For the variable ‘x’, it is equivalent to its new variate u.
U
𝑥−𝑎
=
𝑏
where a  assumed mean
X-a  change in origin
b change in scale
Similarly,
And for the variable ‘y’, it is equivalent to its new variate v.
V
𝑦−𝑐
=
𝑑
Similarly,
Rank Correlation Coefficient :
In statistics, a rank correlation is any of several statistics that measure an ordinal
association—the relationship between rankings of different ordinal variables or different
rankings of the same variable, where a "ranking" is the assignment of the ordering labels
"first", "second", "third", etc. to different observations of a particular variable. A rank
correlation coefficient measures the degree of similarity between two rankings, and can
be used to assess the significance of the relation between them. And the formulae for the
rank Correlation Coefficient is given by :
Rank Correlation Coefficient in Repeated Case