CORRELATION, Degrees of Correlation, Methods of Estimating Correlation

🚩Timestamps:-

00:14 Session Agenda

01:32 What is Correlation?

05:37 Relationship between Two Variables may just be a Coincidence

09:19 POSITIVE AND NEGATIVE CORRELATION

14:55 LINEAR AND NON-LINEAR CORRELATION

18:39 SIMPLE AND MULTIPLE CORRELATION

20:12 Degree of Correlation 

25:29 Correlation and Causation

29:52 Methods of Estimating Correlation

30:22 Concluding Remarks

Learning Outcomes:-

Through this module, you will gain understanding on:-

1.    What is Correlation?

2.    Relationship between Two Variables may just be a Coincidence

3.    POSITIVE AND NEGATIVE CORRELATION

4.    LINEAR AND NON-LINEAR CORRELATION

5.    SIMPLE AND MULTIPLE CORRELATION

6.    Degree of Correlation 

7.    Correlation and Causation

8.    Methods of Estimating Correlation

What is Correlation?

It is a statistical method or a statistical technique that measures quantitative relationship between different variables, like between price and demand.

·         for discovering and measuring the relationship of a quantitative nature and expressing it in a brief formula

 

there is said to be correlation, Whenever some definite connection exists between the two or more groups, classes or series or data

 

In real life however, two or more than two statistical series may be found to be mutually related. For instance, change in price leads to change in quantity demanded. Increase supply of money causes increase in price level. Increase in level of employment results in increase in output. Such situations necessitate simultaneous study of two or more statistical series.

·         The focus of study in such situations is on the degree of relationship between different statistical series. The statistical technique that studies the degree of such relationships is called the technique of correlation

 

Relationship between Two Variables may just be a Coincidence

One may find a relationship between two variables which is just a coincidence. Example: When there is a departure of migratory birds from a sanctuary, you may find a fall in wedding ceremonies in the country. Such relationships are meaningless. These are in other words, spurious relationships which are devoid of any meaningful conclusion. Such relationships are not to be treated as correlations.

·         Only those relationships are be treated as correlations which offer some meaningful conclusions. Example: Increase in rainfall and increase in rice production is a relationship that makes sense; increase in per capita income and decrease in death rate is a meaningful relationship; Good percentage of marks in physics may be related to good percentage of marks in mathematics; and so on.

 

POSITIVE AND NEGATIVE CORRELATION

Correlation between different variables may either be positive or negative. 

(1) Positive Correlation 

When two variables move in the same direction, that is, when one  increases the other also increases and when one decreases the other also  decreases, such a relation is called positive correlation.  Relationship between price and supply may be cited as an example. 

·         Simultaneous Increase or Decrease in the Values of both Variables

 

(2) Negative Correlation

When two variables change in different directions, it is called negative  correlation. Relationship between price and demand, may be cited as an  example.

·         Rise in the Value of One Variable is accompanied  with a fall in the other

 

What does Correlation Measure?

·         Correlation just measures the degree and intensity of relationship between  the two variables, with or without any cause and effect relationship.

Of course the  established relationship between the variables should be capable of offering us some  meaningful conclusion. Example: Students who are good in academics may be good in  sports also. Certainly, it is a meaningful relationship (or correlation) if one finds it. But  surely there is no cause and effect relationship between the two variables

 

LINEAR AND NON-LINEAR CORRELATION

(1) Linear Correlation

When two variables change in a constant proportion, it is called linear  correlation.

If the two sets of data bearing fixed proportion to each other are shown on a graph paper, their relationship will be indicated by a  straight line. Thus, linear correlation implies a straight line relationship.

a	2	4	6	8	10	12	14
b	5	10	15	20	25	30	35

Thus, for every change in variable (a) by 2 units there is a change in   variable (b) by 5 units

 

(2) Non-linear Correlation

When the two variables do not change in any constant proportion, the  relationship is said to be non-linear. Such a relationship does not form a  straight line relationship.

a	2	4	6	8	10	12	14
b	3	7	12	18	25	35	45

Here there is no specific relationship between the two variables, though   both tend to change in the same direction. That is, both are increasing,   but not in any constant proportion.

 

SIMPLE AND MULTIPLE CORRELATION

 (1) Simple Correlation

implies the study of relationship between two variables  only. Like the relationship between price and demand or the relationship   between money supply and price level.  

 

(2) Multiple Correlation

When the relationship among three or more than three variables is  studied simultaneously, it is called multiple correlation. In case of such   correlation, the entire set of independent and dependent variables is   simultaneously studied. For instance, effects of rainfall, manure, water,   etc., on per hectare productivity of wheat are simultaneously studied.  

 

Partial Correlation 

When more than two  variables are involved   and out of these the   relationship between only   two variables is studied   treating other variables   as constant, then the   correlation is partial.

 

Degree of Correlation 

Degree of correlation refers to the Coefficient of Correlation. (r)

 

degree	positive	Negative
Perfect	+1	-1
High	Between + 0.75 and +1	Between -0.75 and -1
Moderate	Between + 0.25 and + 0.75	Between -0.25 and -0.75
Low	Between 0 and + 0.25	Between 0 and - 0.25
zero	0	0

 

(1) Perfect Correlation: two variables change in the same proportion

 

·         Perfect Positive: when proportional change in two variables is in the same direction. In this case, coefficient of correlation is positive (+1).

·         Perfect Negative: when proportional change in two variables is in the opposite direction In this case, coefficient of correlation is negative (-1).

 

(2) Absence of Correlation: there is no relation between two series variables, that is, change in one has no effect on the change in other

 

(3) Limited Degree of Correlation: In real life, one mostly finds limited degree of correlation. Its coefficient (r) is more than zero and less than one (r> 0 but < 1). The degree of correlation between 0 and 1 may be rated as:

·         High: When correlation of two series is close to one, it is called high degree of correlation. Its coefficient lies between 0.75 and 1.

·         Moderate: When correlation of two series is neither large nor small, it is called moderate degree of correlation. Its coefficient lies between 0.25 and 0.75.

·         Low: When the degree of correlation of two series is very small it is called low degree of correlation. Its coefficient lies between 0 and 0.25.

All these degrees of correlations may be positive or negative.

 

Correlation and Causation

·         Correlation is a numerical measure of direction and magnitude of the mutual relationship between the values of two or more variables.

·         But the presence of correlation should not be taken as the belief that the two correlated variables necessarily have causal relationship as well.

·         Correlation does not always arise from causal relationship but with the presence of causal relationship, correlation is certain to exist.

 

Methods of Estimating Correlation

(1) Scattered Diagram Method

(2) Karl Pearson's Coefficient of Correlation

(3) Spearman's Rank Correlation Coefficient.

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What is Correlation, Relationship between Two Variables may just be a Coincidence, POSITIVE AND NEGATIVE CORRELATION, LINEAR AND NON-LINEAR CORRELATION, SIMPLE AND MULTIPLE CORRELATION, Degree of Correlation, Correlation and Causation, Methods of Estimating Correlation

| Correlation | 11th Commerce | by @statomics11comm

 

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