The Relationship Between Least Square and Linear Programming
Adnan ShamkiJaber
Assistant Prof.
Faculty of administration and Economic
Babylon university
Abstract
The predication is important tool for planning where the aim of any statistician is to predicate the values of dependent variable which minimize the error (the different between actual and predicated value).
The least square method is classical method which used to achieve this purpose.
The predication by using least square method depends on minimizing the sum square of errors.
This paper introduces the restrictions of least square method,while
The predication by using linear programming method depend on the assumation of minimizing the sum of absolute errors
1-The predication by using least square method
The estimation of parameter model B_j ,j=1,2,…,k
Of least square method defined as follow:-
Min z=e_1^2+e_2^2+?+e_n^2
s.t:
B_0+B_1 x_i1+?+B_k x_ik+e_i=y_?(i , i=1,2,…,n@)
B_j,e_i unrestricted in sign
2-The predication by linear programming method
Thepredication formula by using this method depend on the assumation:
Min z=|e_1 |+|e_2 |+...+|e_n |
So ,to estimate the parameter model B_jsuppose
e_i=e_i^+-e_i^-
Because ei unrestricted in sign also , the restriction of linear programming method is nonnegative variables (B_j)
So, the model becomes as follow:-
Min z=e_1^++e_1^_+?+e_n^++e_n^-
s.t:
B_0+B_1 x_1i+?+B_k x_ik+e_i^+-e_i^-=y_i
B_j unrestricted in sign
e_i^+,e_i^-?0