By multiple regression we mean a change in the value of a dependent variable due to the combined effect of the changes in the value of the two or more independent variables at the same time. In such a regression analysis we estimate the value of a variable in terms of all other related variables without keeping any of them constant or defunct.
The objectives of a multiple regression analysis are as follows:
(i) To construct an appropriate regression equation to estimate the values of a dependent variable from the values of two, or more independent variables.
And (ii) To set up a standard error of the regression estimates to test the significance of the difference between the observed value and the estimated value.
The multiple regression analysis introduced as above is based on the following assumptions:
(i) The dependent variable is a random variable, and the independent variables may, or may not be random.
(ii) There lies a linear relationship between the dependent, and the independent variables.
(iii)All the variances of the conditional distributions of the dependent variable with the various combinations of the independent variables are equal.
(iv)The conditional distributions for the dependent variable follow the line of a normal probability distribution.
(v) There lies inter-action between the independent variables.