There are different types of correlation which may be noted between any two, or more variables, These different types may be ramified into the following classes:

(i) Simple, Partial, and Multiple correlation.

(ii) Positive, and Negative correlation.

(iii) Perfect, and Imperfect correlation.

(iv) Linear, and non-linear correlation.

##### (i) **Simple, Partial, and multiple Correlation. **

When the relationship between any two variables only is studied, it is a case of simple correlation. When the relationship between any two out of three, or more variables is studied For example, if out of the three related variables, say, marks in Statistics, Marks in Accontancy, and marks in English, we study the correlation between the two variables viz. marks in statistics, and marks in Accountancy ignoring the effect of the other variables i.e. marks in English, it will be a case of partial correlation. On the other hand, when the relationship between any two, or more variables is studied at a time, it is a case of multiple correlation. For example, if we study the relationship between the volume of profits, volume of sales, and the volume of cost of sales at a time, it will be a case of multiple correlation. In actual practice, however, the study of multiple correlation is not popular.

##### (ii) **Positive, and negative correlation. **

When the value of both the variables under study move in the same direction, i.e. with an increase in the value of one variable, the value of the other variable increases, and with a decrease in there value of one variables, the value of the other variable decreases, it is a case of positive correlation. On the other hand, when both the variables under study move in the opposite direction, i.e. and increase in the value of one is followed by a decrease in the value of the other, and a decrease in the value of one is followed by a decrease in the value of the other, and a decrease in the value of one is followed by an increase in the value of the other. It is a case of negative correlation. It is to be noted that the data of positive correlation when plotted on a graph paper will give an upward curve whereas the data of negative correlation, if plotted on a graph paper will give a downward curve. The following data illustrate the examples of positive, and negative correlation.

Sales profits |
54 |
76 | 88 | 109 | 1211 | 1513 |
2015 |

**1.Example of positively correlated data**

##### (iii) **Perfect and imperfect correlation. **

When the values of both the variables under study change at a constant ratio irrespective of the direction, it is a case of perfect correlation. On the other hand, when the values of the variables under study change at different ratios, it is a case of imperfect correlation. When correlations are measured mathematically, the value of perfect correlation will be either + 1 or -1 ,and the value of imperfect correlation will be between ± 1 . Thus, perfect correlation can either be of perfect positive, or perfect negative nature. Similarly, imperfect correlation can either be of imperfect negative nature. It is to be noted that the perfect, and imperfect correlations speak of the degree of correlation which is ascertained by computing the co-efficient.

##### (iv) **Linear, and non-linear correlation**.

When the data relating to correlation plotted on a graph paper give rise to a straight line, it is a case of linear correlation. This is possible only when there is perfect relationship, or constancy in the ration of changes between the values of the variables. The linear constancy in the ratio of changes between the values of the variables. The linear correlation, again, may be either positive, or negative in nature, and accordingly, it may give either an upward, or a downward straight line when plotted on a graph paper. On the other hand, when the data of two variables plotted on a graph paper give out a curve of any direction, it is a case of curvi-linear, or a non-linear correlation. A curvi-linear, or a non-linear correlation. A curvi-linear correlation appears only when there is imperfectness, or inconsistency in the ration of changes between the values of the variables. Like the linear correlation, non-linear correlation can be either positive, or negative in nature, and accordingly, it may give either an upward, or a downward curve when plotted on a graph paper. The following will illustrate the cases of linear and non-linear correlations.