A linear regression analysis is one which gives rise to a straight line when the data relating to the two variables are plotted on a graph paper. This happens, when the two variables have linear relationship with each other which means that with a change in the value of the independent variable by one unit there occurs a constant change in the values of the dependent variable. The mathematical equation of such straight line (i.e. Y = a + bx) enables us to study the average change in the value of the dependent variable for any given value of the independent variable. The linear relationship is usually taken into account because of its simplicity and better prediction. Besides, a linear trend can be easily projected into the future on the basis of such relationship.
A non-linear regression analysis, on the other hand, is one which gives rise to a curved line when the data relating to two variables are plotted on a graph paper. In such a case, the regression equation will be a function involving the terms of higher order like, Y = X2 , Y = X3 etc. These equations are not very useful for prediction purpose although, they are used for interpolation and some other mathematical operations.