A simple regression analysis is one which is confined to only two variables say, X and Y or Price and Demand, or Advertisement expenditure and Volume of sales etc. In such cases, the value of one variable is estimated on the basis of the value of another variable. The variable whose values are estimated is called dependent, regressed or explained variable, and the variable that serves as the basis of determining the value of the other variable is called the independent, regressing, or explanatory variable. For example, if the expenditure on advertisement can have some effect on the volume of sales, then advertising will be the independent variable and sales will be the dependent variable. In such a case, representing the sales by Y and advertising by X, the functional relationship between sales and advertising can be expressed as Y = f (x).
A multiple regression analysis, on the other hand, is one which is made among more than two related variables at a time say, X, Y, and Z or say, over Sales, Price and Income of the people. In such analysis, the value of one variable say, price of goods and Income of the consumers. Here, one variable is made dependent and the other variables independent. The functional relationship in such a case is expressed as under :
Y = f(X, Z,) or X = f(y, z), or Z = f(X, Y)