Developing a Prediction Model to Predict the Construction Project Cost by Using Multiple Linear Regression Technique

Objectives: Prediction cost of construction project requires large information and data about the project. This makes the prediction cost very complex at the early stage because of limitation of data and information at this stage. The aim of the study is building prediction model to predict cost of construction project in Iraq. Method: To develop the prediction model, Multiple Linear Regression technique (MLR) with Weighted Least Square (WLS) was used. The researcher use 501 set of historical cost data gathered in Iraq for period (2005-2015) for developing the model. The cost of twenty five items of project are used for cost forecasting by MLR model and they involved cost of (excavation the foundation works, Landfill works, filling with sub-base works, Construction works under moisture proof layer, Construction works above moisture proof layer, Construction works of sections, ordinary concrete for walkways, reinforced concrete foundation, reinforced concrete column, reinforced concrete lintel, reinforced concrete slabs, reinforced concrete beams, reinforced concrete stair, reinforced concrete for the sun bumper, plaster finishing works, cement finishing works, Plastic Paints, Pentellite paints, Stone packaging, Works of placing marble, Ceramic works for floor, Ceramic works for walls, Flattening (two opposite layers of lime ), Flattening (Tiling). Findings: The result shows that MLR with WLS has the capability to predict construction cost with a height coefficient of correlation 95.8%, degree of accuracy 98.97% and smallest mean absolute percentage error 1.03%. Applications: MLR with WLS have shown to be a promising method for using in the initial stage of construction projects when only limited data and incomplete information set is preparing for cost analysis.


Introduction
Construction manager consider cost is very important factor. If the construction project matching the budget with the cost, schedule on time and quality determined by the employer then the project is considered success 1 . When using a weak strategy or inappropriate budget or schedule forecasting the project may be failure 2 . Therefore, the success of any construction project depends on the accurate estimation cost 3 . Accordingly, estimation cost in initial phase has important role in any construction project 4 .
Because of importance of estimation cost in early phase and limited data during the early stage of construction, construction managers leverage their experience, knowledge and estimators to estimate cost of project. As such, intuition plays an important role in decision-making 2 .
Many researches were attempted to predict the cost of construction 5 . In 6 developed models by using multiple linear regression techniques to estimate initial cost of road projects features such as soil conditions, soil drill ability and terrain conditions. In 7 develop models for estimating the construction cost of buildings by using Multiple Regression Techniques. The researcher use 286 sets of historical data gathered from the United Kingdom. They establish 41 independent variables, the researcher uses five important variables such as gross internal floor area (GIFA duration, function, piling and mechanical installations in all six models. In 8 develop models by utilities MLR to estimate productivity of marble finishing work by using 100 set of historical data gathered in Iraq for various kinds of construction projects. The researcher concludes that MLR have the capability to estimate the productivity for finishing works with height degree of accuracy. A recent study 9 used MLR to develop model for estimating the cost of communication projects in Iraq. The data that used to develop model were 45 construction projects. They used several significant independent variables that act on communication for developing MLR model. From the result, the researchers found regression analysis techniques proven its ability to prediction cost with very height of accuracy.
The scope of the study is using multiple linear Regression technique to developing and assesses a prediction model that can used to predict the final cost of projects, through the procedure below: • Determination input and output for model. • Using the MLR to develop a mathematical prediction model to predict the budget of project. • Cheek the developed model by making the verification and validation through calculate the degree of accuracy of model and the coefficient of correlation between real cost and prediction cost.

Methodology of Study
Methodology of this study divides to theoretical work and field work: • Theoretical part: This includes the review of literatures that associated to cost estimation concept and multiple linear regression analysis and its utilization in prediction the budget of construction projects. • Field part: This includes data collection, data analysis and choosing of inputs, then building the prediction Model. And validation this Model.

Application of MLR
M any reference clarified the concept of MLR technique. The research submitted by 8 explain this technique in an easy way. Multiple linear regression considers strong powerful technique that can use as prediction tool and help the engineers and researchers to know the correlation between input and output variables. It can tentatively frame 10 : • xi1 and xi2 are independent value • yi the desired output.
• ei the error components are supposed to be in normal variables with mean zero and variance σ2. and a0, a1, ….,ap are unknown regression coefficient.

Weighted Least Square Regression
WLS has not specific type of equation to know the correlation between input and output variables, contrasting the linear and nonlinear regression that is associated to an equation. This type of regression used with equation that linear or nonlinear in parameters. It is working by weights that connected with each observation, into the fitting criterion. Weight value refers to the accuracy of information contained in the associated observation. Improving the weighted fitting criterion to obtain the parameter estimates permits the weights to define the contribution of each observation to the last parameter estimates. It is significant to observe that the weight for each observation is given relative to the weights for another observation; so different sets of absolute weights can have identical special effects 11 . The researcher use WLS to determine the regression coefficient.

Input and Output for Model
Model input (independent variable) variables for cost estimation model were consisting of twenty five variables are cost of excavation the foundation works, Landfill works, filling with sub-base works, Construction works under moisture proof layer, Construction works above moisture Vol 12 (7)

Development MLR
The software employed to develop the MLR model is Statistical Package for the Social Sciences version 24. Table 1 shows the statistical analysis of data. Backward elimination method is implemented to develop the regression model. The procedure of this method is to enter all input variables in the model equation and then gradually excludes. The input that has least partial correlation with the output variable is considered first for removal as shown in Table 2.

Model Validation
Model validation is very important step in building a cost model to test its accuracy it includes testing and evaluating the developed model with some validation or test data. The validations data is taken randomly from the data set and should not enter in model develop. The researcher used 30% of data to cheek accuracy of model. To evaluate the validity of the derived equation of the model for the final cost of construction projects, the natural logarithm (Ln) of prediction cost is draw beside the natural algorithm (Ln) of real cost for test data set as shown in Figure 1. The coefficient of determination (R 2 ) is obtained to be (91.8%), so it can be decided that this model shows a very good agreement with the real observations.
The same statistics parameters that use 13 is used in this research to establish the average accuracy of developed model, as shown in the Table 4, where the Mean Absolute Percentage Error (MAPE) equal to 1.03% that mean the Average Accuracy (AA) of this model equal to 98.8 % is very good as shown in the Table 4.

Conclusion
The researcher concludes some point from study as shown below: 1. The regression analysis technique proved its ability for prediction of the budget of construction Projects. One prediction model is built and the result showed that it is very accurate as the degree of accuracy was 98.97%. 2. Coefficient of determination is utilizing for determining the linear relationship between real cost and predict cost with 91. 80%. 3. The developed model can be used by the stakeholders to predict the cost of construction since it is simple and easy to use.