A total regression analysis is one which is made to study the effect of all the important variables on one another. For example, when the effect of advertising expenditure, income of the people, and price of the goods on the volume of sales are measured it is a case of total regression analysis. In a such cases, the regression equation takes the following forms like that of a multiple regression analysis.
S = f (A,I,P) and X= f ( Y,Z,P) etc.
This type of regression analysis is usually made in the field of business and economics where values of a variable are effected by multiplicity of causes.
A partial regression analysis, on the other hand, is one which is made to study the effect of one, or two relevant variables (excluding the irrelevant one) on another variable. The equation of such a regression takes the following form like the total simple regression analysis:
Y = f (X but not of Z and P)
S = f ( advertisement but not of price and income of the people)