MULTIPLE REGRESSION

The least square regression equation discussed above was based on the assumption that total cost was determined by only one activity based variable. However, other variables are likely to affect labour costs such as labour hours, material costs, machine hours, etc. These may have an effect on labour costs.

The equation for the simple regression can be expanded to include more than one independent variable as shown below:

Y = a + b₁X₁ + b₂ X₂ + b₃ X₃ +………+b_n X_n

For two independent variables, the function will be of the form:

Y = a + b₁X₁ + b₂ X₂

The normal equations can be given by:
∑y      = na + b₁ ∑X₁ + b₂∑x₂
∑X₁Y  = a∑x₁ + b₁∑X₁₂ + b₂ ∑X₁ ∑X₂
∑X₂ Y = a∑x₂ + b₁∑  X 1∑X₂ +b₂ ∑X₂ 

Normally computers are used for the solution of multiple regression.