Parametric estimation of construction cost using combined bootstrap and regression technique

Proceedings of the International Conference on Emerging Trends in Engineering and Management (ICETEM14)
30 – 31, December 2014, Ernakulam, India
201
PARAMETRIC ESTIMATION OF CONSTRUCTION COST
USING COMBINED BOOTSTRAP AND REGRESSION
TECHNIQUE
[1]
Ms. Saira Varghese, [2]
Dr. S.Kanchana
[1], [2]
Civil Engineering, RVS Technical Campus-Coimbatore/Anna University-Chennai/India
ABSTRACT
This paper presents a parametric estimation approach for the prediction of future construction cost. In the
proposed method, a combined regression analysis and bootstrap re-sampling technique is used to develop the range
estimate for construction costs. In parametric estimating, a model including the important parameters is developed to
predict construction costs, using data of previous projects and the regression analysis is used to determine an adequate
cost model. The regression models can be generated using software’s like SPSS (Statistical Package for Social Sciences)
and MS Excel. This study is of relevance to practitioners and researchers for conceptual estimation of construction costs.
Keywords: Coefficient of Determination, Construction Project, Cost Significant Model, Estimation Cost, Parametric
Estimation Regression Analysis.
1. INTRODUCTION
Every project has a certain objective (scope), has defined start and end dates (schedule) and has funding limits
(budget). This defines the border of a construction project. Since budget and schedule are the main project constraints to
be worked with, any estimation concerned with cost and duration are very helpful in the early stages of construction
project management process. Construction cost estimating is essential for all of the stakeholders of a construction project,
for an ordinary project, namely they are owner, designer, contractor and subcontractor.
Construction cost estimation can be defined as “an effort to forecast the actual cost”. Cost estimations can be
done in any stage of the project. When the project delivery stages of a construction project are considered, the process
can be summarized in 5 different stages:
1. Feasibility Stage
2. Conceptual Stage
3. Engineering
4. Procurement
5. Construction & Turnover
Conceptual (early) cost estimation is performed in Conceptual Stage before detailed design is completed. In
Conceptual Stage, the preliminary design of the project has been finished. Preliminary drawings and specifications are
the only sources that can be used in conceptual cost estimation. For an accurate estimate, detailed scope definition is
essential. At the early stages of a construction project the design information and scope definitions are very limited,
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
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ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 5, Issue 12, December (2014), pp. 201-205
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hence achieving high accuracy is very difficult. As the project proceeds from Feasibility Stage to Turnover Stage, the
accuracy of cost estimating increases due to the finalized drawings and specifications.
Conceptual cost estimating methods are;
1. Unit Cost Method
2. Factor Method
3. Probabilistic Modelling & Simulation
4. Parametric Estimation
Parametric estimation uses the historical data of projects. In this method, the cost of a project is tried to be
expressed in terms of different parameters. The parametric cost estimation models are used to express a dependent
variable (cost) in terms of independent variables (parameters). By implementing probabilistic modeling & simulation and
parametric estimation methods, it is possible to produce conceptual (early) cost range estimates. By range estimating, the
risk is captured by giving a range of estimations as a function of desired confidence. When regression models are decided
to be used, there is always the problem of determining the class of relations between parameters and project costs. It is
hard to find the accurate relation between dependent (cost) and independent variables (parameters) when there are
multiple cost components. Regression model is a parsimonious model. A parsimonious model can be defined as: “a
model that fits the data adequately without using any unnecessary parameters”.
Since conceptual cost estimations of projects are employed in the early stages, by implementing point estimates,
it is not possible to take into account the uncertainty in the estimations. The variability included in the estimations should
be emphasized by providing range estimates. In this context, the main purpose of this study is to develop a method for
early range estimations of costs by using regression analysis and bootstrap technique. To implement this study, data of a
building project was taken with detailed cost estimation and applied to the analysis as the sample set.
2. BOOTSTRAP TECHNIQUE
2.1 History
The bootstrap method introduced in Efron (1979) is a very general re-sampling procedure for estimating the
distributions of statistics based on independent observations. The bootstrap method is shown to be successful in many
situations, which is being accepted as an alternative to the asymptotic methods such as the traditional normal
approximation.
2.2 Approach
Bootstrap is a viable alternative to asymptotic standard errors and confidence intervals.
In statistics, bootstrapping is a method for assigning measures of accuracy to sample estimates. This technique
allows estimation of the sampling distribution of almost any statistic using only very simple methods.
Bootstrap is a re-sampling method in which r new samples, each the same size as the observed data, are
randomly drawn with replacement from the observed data. The purpose of bootstrap is to mimic the process of sampling
observations from the population by re-sampling data from the observed sample. Bootstrap methods are more flexible
than classical statistical methods as they require fewer assumptions.
Regression analysis and bootstrap re-sampling method were combined in order to develop range estimates for
construction costs of building projects. The combination of regression and bootstrap techniques to integrate parametric
and probabilistic estimation methods was explained as follows: A simple linear model with one parameter p, for cost
item m was showed as;
cm = α0 + α1p ------------------------- (1)
Where, cm = predicted cost,
α0 and α1 = regression coefficients, and
The regression parameters α0 and α1 were estimated by using the observed data x = (x1, x2, ... , xn). The
observed data pairs x = {(cm1, p1), (cm2, p2), … , (cmn, pn)}, compiled from previous projects for cost item m, with one
parameter p, were re-sampled by bootstrap method, to form a data set x*. Integers i1, i2, … , in, each of which has a value
between 1 and n, with a probability of 1 / n were selected randomly to perform re-sampling. The bootstrap data set x* =
{(cmi1, pi1), (cmi2, pi2), … , (cmin, pin)} was formed.
The star notation was used to indicate that x* is not the actual data set x, but rather a resampled version of x. The
bootstrap data set (x*1, x*2, … ,x*n ) formed consists of members of the original data set (x1, x2, ... , xn). After the
formation of bootstrap data set, x* was used to determine the regression coefficients for the model. One of the main
targets was to gain the benefit of bootstrap approach by including advantages of probabilistic and parametric estimation
methods at the same time since the bootstrap method requires fewer assumptions when compared to classical statistical

203
techniques. When using bootstrap method any assumptions regarding the distribution of the error term ε, and the
distributions of the cost items are not needed. Also by using the bootstrap technique, an effective method to integrate the
information of the cost items and parameters for range estimating of the total project cost, was developed.
3. REGRESSION TECHNIQUE
In regression problems, case resampling refers to the simple scheme of resampling individual cases - often rows
of a data set. For regression problems, so long as the data set is fairly large, this simple scheme is often acceptable.
A regression analysis is proposed which assumes a cause-and-effect relationship between the variables. In a
simple regression, there is one dependent and one independent variable whereas in multiple regressions there is one
dependent and at least two independent variables. A linear relationship between the dependent and independent variables
is assumed. An error term U is added in the regression model for capturing the effect of the omitted variables. The
estimation of the regression model is carried out by the ordinary least squares (OLS) method. The OLS method aims at
minimizing the error sum of the squares while estimating the regression model.
A test is conducted for testing the significance of the individual regression coefficients. The overall fit of the
regression is given by R² that is called the coefficient of determination and is a measure of the explanatory power of the
model. The value of R² lies between 0 and 1 (both values inclusive). The closer the value of R² to one, the better is the
goodness of fit. The significance of R² is carried out by using the F statistic. The use of regression in estimating the point
and interval prediction is shown. Also is demonstrated the computation of elasticity and its use in decision making.
4. COMBINED PARAMETRIC BOOTSTRAP AND REGRESSION TECHNIQUE
4.1 Parametric bootstrap
In this case a parametric model is fitted to the data and samples of random numbers are drawn from this fitted
model. Then the quantity, or estimate, of interest is calculated from these data. This sampling process is repeated many
times as for other bootstrap methods. The use of a parametric model at the sampling stage of the bootstrap methodology
leads to procedures which are different from those obtained by applying basic statistical theory to inference for the same
model.
4.2 Parametric Methods or Parameters
The cost estimating model used in design phase must be in coherence with the definition report of the project. It
is then better to consider the concept of product architecture. We have not known yet how these products will be
produced, but we can access a number of physical characteristics or parameters like the mass, the volume, the energy
absorbed or the number of input-output. This is obtained for information purposes at the Beginning of development
phase.
The parametric estimate has been constructed specifically to create from these parameters the costs to estimate.
We must go from high techniques characterizing the product and owned by the design engineer to economic data
necessary for management.
Two main types of parametric methods are to be high-lighted; they differentiated both by their design and usage.
a) The cost list;
b)The statistical models or cost estimates formula.
This method involves more complex calculations than the analogy method. It only works on family products (or
projects) of identical structure differing only in size. The calculations are automated on a spreadsheet such as Excel. The
use of the application of parametric assessment can be within reach of an unskilled operator .On the contrary, the
development of cost estimation formula is complex and requires an expert experienced in statistical calculation.
This method is very practical to conduct appropriate testing in an activity cost analysis. It is appropriate to be
used at the time of the unavailability of data and information to make the cost estimation process more accurate. One of
parameters method that frequently used to indicate the relationship between costs and the variable is a linear curve.
The formula that shows the cost relationship with independent variables, namely:
Y = a x --------------------------------(2)
Where, Y = Project cost (dependent variable)
a = Parameter value
x = Variable (independent variable)

204
Explanation of the formula above is as follows:
Project Cost:- It is the result of a project estimate that is used to determine the relationship between the costs of the
various parts of the project.
Parameter Value:- Parameter value is the regression coefficient (can use SPSS). Based on the number of parameters that
vary on each building project, then in future studies, we can include the other parameters that are assumed to represent all
the parameters that exist in every building project.
These parameters include:
a1 = Parameter value for reinforced concrete work
a2 = Parameter value for roof structure and roof covering work
a3 = Parameter value for timber structure and ceilings work
a4 = Parameter value for sills/frames, doors, windows, and partitions work
a5 = Parameter value for floor work and coating work
Variable:- In statistical science, generally consisting of two variables, the Y variable and X variable. The relationship
between two variables (Y and X) will produce a linear regression equation.
Regression models are used to express a dependent variable in terms of independent variables. The main idea of
regression analysis is to fit a curve for the given data while minimizing the sum of squared error and maximizing the
coefficient of determination (R2
).
5. COST SIGNIFICANT MODEL
Viewed from the side of construction, this is the necessary budget plan to complete a project and it is a cost that
has been set, based on the results obtained. Plan of budgeting in the construction process is generally intended to estimate
the amount of financing a project, not a real cost (actual cost) to be spent. Cost model can be used to organize and
distribute the cost estimation or estimated costs into functional areas that can be defined and calculated quantities. The
most common ways to find out the cost of a building is a parameter method. This is most often used for project feasibility
studies.
The cost model is the latest technique used in cost estimating on a project being proposed. A mathematical
model or formula shows that best describe the data collected in the form of cost or price. Another technique often used is
single linear regression analysis, which is representative of cost models, despite the fact shows that a more appropriate
technique is simulation.
6. SPSS SOFTWARE
The abbreviation of SPSS is “Statistical Package for Social Sciences”. SPSS is a Windows based program that
can be used to perform data entry and analysis and to create tables and graphs. SPSS is capable of handling large
amounts of data and can perform all of the analyses covered in the text and much more. SPSS is commonly used in the
Social Sciences and in the business world, so familiarity with this program should serve you well in the future. SPSS is
updated often.
7. MICROSOFT EXCEL
Excel is the spreadsheet program created by Microsoft. The instructions given here are specific. The
information given in this quick tutorial is meant to give a working knowledge of how to use Excel. There are usually
several different ways to perform the same function in Excel and several functions can be performed.
The validation part of the project thesis is done by using Microsoft Excel. The single linear regression equations are
created in the spreadsheet and the models are tested in the excel sheet.
8. CONCLUSION
Parametric and probabilistic estimating techniques were integrated using regression analysis and bootstrap
methods. The bootstrap method doesn’t require any assumptions regarding the probability distribution of the model
errors, or the distributions of the cost items, and can be implemented by using a spreadsheet program. Integration of
parametric and probabilistic estimating techniques will hopefully lead to more realistic cost expectation during early
project stages.
The implementation of bootstrap method for conceptual cost estimating offers several advantages over the
classical statistical techniques. The non-parametric bootstrap avoids restrictive and sometimes dangerous assumptions

205
about the form of underlying populations. In addition to cost estimating, potential implementation areas of bootstrap in
construction management include risk analysis, probabilistic scheduling, and simulation of construction operations and
modelling and hypothesis testing applications.
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