Comparison “New Square Method” and “Least Square Method”

If Equation 1 as shown below is adopted to fit any data:

                                              Equation 1 

 The Comparison Table between the “New Square Method” and the “Least Square Method”:

1. In the “new square method”, the power valueof the dependent variable is calculated, while in the “least square method”, is assumed to be 1. With the calculated power value for the dependent variable, the new square method is able to have the fitted equation generate a fitted line at any curve to better fit the non-linear data. 

2．In the “new square method”, non-linear data with one factorcan be regressed by applying the following Equation 2 in the computer programs to obtain more accurate fittings of non-linear data by regression models.

        Equation 2

In Equation 2:

— Variable.

— Function.

—Dimensional (two-dimensional).

— Element.

— Constant.

— Coefficient.

— Power.

3．As for the regression of non-linear data with multi-factors in the “new square method”, the following Equation 3 can be utilized in computer programs for this purpose. This equation takes into account both the contribution of factors to the objective function () and the interplays among factorsduring the regression calculation, that is why the fitted models are of high correlation.

  Equation 3

In Equation 3:

— Variable.

— Function.

— Dimensional (three-dimensional).

— Element.

— Constant.

— Coefficient.

— Power.

Note: Equation 9, which takes three-dimensional data as its example, can be applied for the regression of data in curved surface data.