Correlation is a measure of the amount of association existing between two variables. For linear correlation, if points are plotted on a graph and all the points lie on a straight line, then perfect linear correlation is said to exist. When a straight line having a positive gradient can reasonably be drawn through points on a graph positive or direct linear correlation exists, as shown in Fig. 59.1(a). Similarly, when a straight line having a negative gradient can reasonably be drawn through points on a graph, negative or inverse linear correlation exists, as shown in Fig. 59.1(b). When there is no apparent relationship between co-ordinate values plotted on a graph then no correlation exists between the points, as shown in Fig. 59.1(c). In statistics, when two variables are being investigated, the location of the co-ordinates on a rectangular co-ordinate system is called a scatter diagram-as shown in Fig. 59.1.
The amount of linear correlation between two variables is expressed by a coefficient of correlation, given the symbol r. This is defined in terms of the deviations of the co-ordinates of two variables from their mean values and is given by the product-moment formula which states: coefficient of correlation,