*2.2. Determination and Prioritization of Factors Using ANN*

After training the network, output coefficients of introduced variables can be extracted from MATLAB software. As the artificial neural network considers all the introduced factors important, the prioritization of factors is conducted according to the coefficients.

*Symmetry* **2020**, *12*, x FOR PEER REVIEW 5 of 17

**Figure 2.** Schematic structure of the Artificial Neural Network (ANN).

#### **Figure 2.** Schematic structure of the Artificial Neural Network (ANN)**.**  *2.3. Earned Value Prediction Using Multiple Regression Method*

*2.2. Determination and Prioritization of Factors Using ANN*  After training the network, output coefficients of introduced variables can be extracted from MATLAB software. As the artificial neural network considers all the introduced factors important, the prioritization of factors is conducted according to the coefficients. The correlation among dependent and independent variables can be determined using the multiple regression method [62]. There are four methods to enter input data into the model. These methods are the entering method (direct method), backward method, forward method and step-wise method [63]. In this study, the direct entering method was selected to be exploited. The linear relationship among the variables is illustrated below:

$$y\_i = b\_0 + b\_1 \mathbf{x}\_{i1} + \dots + b\_p \mathbf{x}\_{ip} + e\_i \tag{3}$$

multiple regression method [62]. There are four methods to enter input data into the model. These methods are the entering method (direct method), backward method, forward method and step-wise method [63]. In this study, the direct entering method was selected to be exploited. The linear where *p* is the number of predictions, *b <sup>j</sup>* is the value of the *j*th coefficient, *xij* is the *i*th value of the *j*th prediction, and *e<sup>i</sup>* is the error of the *i*th value. Furthermore, the matrix form of the model is presented as follows:

The correlation among dependent and independent variables can be determined using the

$$\mathbf{Y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\varepsilon} \tag{4}$$

 = + ଵଵ +⋯+ + (3) where is the number of predictions, is the value of the ௧ coefficient, is the ௧ value of where β is the vector of regression coefficients, ε is the matrix of fitting errors, *Y* is the vector of the dependent variable, and *X* is the matrix of independent variables.

the ௧ prediction, and is the error of the ௧ value. Furthermore, the matrix form of the model is presented as follows: = + (4) In order to determine and rank factors affecting the earned value of the studied projects, outputs of SPSS analyses were used. Variables with a significance of less than 0.05 were selected as effective factors. Furthermore, according to their significance value, variables were prioritized.

where is the vector of regression coefficients, is the matrix of fitting errors, is the vector of the dependent variable, and is the matrix of independent variables. In order to determine and rank factors affecting the earned value of the studied projects, outputs Finally, the ANN and the multiple regression model were compared according to the correlation coefficient and mean squared error of each model. The model possessing the higher correlation coefficient, as well as the lower MSE, was introduced as the preferable model [64].

of SPSS analyses were used. Variables with a significance of less than 0.05 were selected as effective
