Correlation & Regression Analysis

1. Introduction and meaning

Here we deal with the distributions consisting of two variables.
Let us see the relation between each of the following pair of variables

i) Income and Expenditure
ii) Price and Demand

In example (i), as the income increase (or decreases), the correspondingly the expenditure will increase (or decrease). That is the two variables income and expenditure are related.

In example (ii), as the price increases ( or decreases), the correspondingly the demand will decrease (or increase). That is the two variables are again related.

The relationship between the two variables such that change in the value of one variable, makes a change in the value of the other variable is known as the correlation. The measure of the degree of correlation between the two variables is known as the "correlation coefficient". It gives the extent to which the two variable are correlated and direction along which the two variables move. But the correlation analysis does not give use the cause and effect relationship. One cannot say that even when there is a high degree correlation, which one is the cause and which one the effect.

Types of Correlation

We have the following types of correlation :

a) positive and negative correlation
b) Linear and non-linear correlation
c) simple,multiple and partial correlation

a) Positive and negative correlation

i) Positive correlation : The correlation between two variables is said to be positive if the two variables move in the same direction. That is, increase (or decrease) in the value of one variable makes increase (or decrease) in the value of the other variable. For example :

i) The investment and the profit

ii) The height and the weight

iii) x: 10 20 30 40

 y:    5    8   10   20

iv) x: 100 50 30 10

    y:     8      5     3     2

ii) Negative Correlation: The correlation between two variables is said to be negative if the two variable move in the opposite direction. That is, increase ( or decrease) in the value of one variable makes decrease ( or increase ) in the value of the other variable. For example :

i) speed and time
ii) volume of production and the price

iii) x : 10 20 25 50
y : 50 20 10 8

iv) x : 100 50 30 10
y : 1 2 3 7

b) Linear and non-linear correlation

i) Linear correlation:
The correlation between two variables is linear when a unit change in the value of one variable makes a constant change in the value of the other variable over the entire range of the values. For example:

                    x:      1     2    3    4    5
                    y:      5     10  15 20 25

ii)Non-linear correlation:
The correlation between two variables is non-linear if there is no constant change in the value of the other variable when there is a unit change in the value of one variable. For example :

         x:   4      5     6     7    8
         y:   12   13   18  20  30

**c) Simple, Multiple and Partial Correlation

i) Simple Correlation: A correlation between two variables is known as a simple correlation. For example :
The area of the land and the volume of wheat grown.

ii) Multiple Correlation
A correlation between three or more variables is known as a multiple correlation.
For example: The amount of rainfall to some extent, the quantity of fertilizer used and the yield of wheat per hector.

iii) Partial Correlation
A correlation Between two of the three or more variables, keeping all the remaining variables constant , is known as a partial correlation. For example :
The amount of rainfall and the yield of wheat per hector, keeping the quantity of fertilizer used constant.

To Be continue.........

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