The distinction between linear and non-linear correlation is based upon the constancy of the ratio
of change between the variables. If the amount of change in one variable tends to be a constant
ratio to the amount of change is the other variable then correlation is said to be linear. For example,
observe the following two variables X and Y.

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

Correlation would be called non-linear or curvilinear if the amount of change in one variable does not bear a constant ration to the amount of change in the other variable. For example, if we double the amount of rainfall the production of rice or wheat, etc., would not necessarily be doubled. It may be pointed out that in most of the practical situations, we find a non-linear relationship between the variables. However, since techniques of analysis for measuring non-linear correlation are far more complicated than those for linear correlation, we generally make an assumption that the relationship between the variables is of the linear type.

The following two diagrams will illustrate the difference between linear and curvilinear correlation:



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