ACCA Paper F2 free course note | Correlation & Regression | Types of Correlation

Correlation is described or classified in several different ways. Three of the most important are

(1) From the viewpoint of inclusion of variables

v  Simple Correlation: Association between only two variables is simple correlation. When only two variables are studied it is a problem of simple correlation. For example, relationship between profit and capital.

v  Multiple Correlation: Association among more than two variables is multiple correlation. In a multiple correlation three or more variables are studied simultaneously. For example, when we study the relationship of profit and capital, production cost and advertisement cost.

v  Partial Correlation: Incase of multiple correlation the association between two variables is called partial correlation when effects of other variables remain constant. In partial correlation we recognize more than two variables. But consider only two variables to be influencing each other, the effect of other influencing variable being kept constant. For example, correlation between capital and profit when the effects of production cost and advertisement cost remain unchanged.

(2) From the view point of direction of variables

v  Positive Correlation: If the change of one variable is associated with the change of other variable is the same direction, then the correlation existing between variable is called positive correlation. For example, if one variable (i,e. investment) is increasing the other (i.e. profit) on an average  is also increasing or, if one variable (i,e. investment) is decreasing the other (i.e. profit) on an average  is also decreasing, then the correlation is said to be positive. 

Investment (X)	Profit (Y)
5	2
10	3
15	4
20	5
25	6

v  Negative Correlation: If the change of one variable is associated with the change of other variable is the opposite direction, then the correlation existing between variable is called negative correlation. For example, if one variable (i,e. supply) is increasing the other (i.e. demand) on an average  is decreasing or, if one variable (i,e. supply) is decreasing the other (i.e. demand) on an average  is  increasing, then the correlation is said to be negative. 

Supply (X)	Demand (Y)
5	25
10	20
15	15
20	10
25	5

v  No correlation: If the change of one variable is no way associated with the change of other variable, then that indicates no relation.

Supply (X)	Demand (Y)
5	5
10	20
15	3
20	50

(3) Linear and Non-Linear

v  Linear Correlation: When the ratio of change in both variables is constant then it is called linear correlation. If the amount of change in one variable tends to bear a constant ratio to the amount of change in other variable then the correlation is said to be linear.

Investment (X)	Profit (Y)
10	70
20	140
30	210
40	280
50	350

It is clear that the ratio of change between two variables is the same. If such variables are plotted on a graph paper, all plotted points would fall on straight line.

v  Non-linear Correlation: When the ratio of change in both variables does not give constant result then it is called non linear correlation. If the amount of change in one variable does not bear a constant ratio to the amount of change in other variable then the correlation is said to be non-linear. For example, if we double the amount of investment, the profit would not necessarily be doubled.

Investment (X)	Profit (Y)
10	70
20	100
30	120
40	150
50	350