ANLY482 AY2017-18T2 Group18/TeamDAcct Project Methodology

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Methodology

Data Preparation:

All the files acquired have helped us deepen our understanding of the company’s business and ultimately the business problem. However, not all files were crucial to formulate recommendations to the business problem on hand. The following are the list of data-sets prepared:

• Master Client Listing

• Facility Details

• Manpower Details

Exploratory Data Analysis

Following which, EDA (e.g. through the usage of graphs or tables of summary measures) was conducted to get a better understanding of the data. From the EDA, we will have a better understanding of the relationship amongst the explanatory variables (factors that drives the expenses such as wages) as well as provide us with a general direction and size of relationship between explanatory and outcome variables. In the analysis of data, we will be using the software SAS JMP Pro 13 as our main tool for data cleaning, data preparation and EDA. Our choice of this software is that it allows us to conduct statistical analysis on big datasets and can generate results that are easy to understand for end users. In addition, due to its popularity of being widely used, tutorials are readily available on the web, should we encounter any problem.

Thereafter, we can formulate and suggest a model to the client that forecast the expenses incurred for an anticipated project site with certain characteristics. From a business perspective, this would point to possible approaches management wish to take (i.e. minimise cost, bid at higher price, pegged to industry price, market share growth), in using our proposed model to assist in shortlisting future project sites and to drive business strategy overall.

Analytical Methods

After cleaning and preparing the data, we decided to work on our confirmatory analysis to assess the appropriateness of the explanatory variables to be used for our regression analysis. Thereafter, we performed multiple linear regression to build an explanatory model to analyse whether an increase in any of the explanatory variables (determined in our confirmatory analysis) has an impact on any of the various cost components incurred for a cleaning project type. The four major cost components that we have identified in a cleaning project are namely:

• Total Project Costs

• Manpower Costs

• Chemical & Materials Costs

• Equipment Costs

For this project, we will be focusing on one specific cleaning project type - conservancy sites (zones).

Confirmatory Analysis

We first analysed the distribution of the explanatory variables identified (dwelling units, market/hawker stalls, commercial units, open car-lots, open motorcycle-lots, multi-storey car-lots, multi-storey motorcycle-lots, bus/lorry lots) that describe the attributes of conservancy zones. These are represented as shown:

Upon closer inspection of the explanatory variables: market/hawker_stalls_edu and bus/lorry_lots_edu, it was found that majority of conservancy zones had zero market/hawker stalls and bus/lorry lots. We decided to categorise these numerical variables by putting the data into discrete categories (called bins). Dummy variables were introduced, where it is coded as 1 for all observations that had – for example, non-zero market/hawker stalls, and 0 for all observations that had zero market/hawker stalls.

The subsequent distribution of the above dummy variables introduced are represented as shown:

From our exploratory data analysis on conservancy project sites, we can see that for several of LS 2’s conservancy project sites that it undertakes, it engages third party (subcontractor) to perform under a subcontract all or part of the work that was included in the original contract won by LS 2. We decided to account for this by introducing a dummy variable, where it is coded as 1 for all observations that were performed in-house (i.e. not subcontracted out), and 0 for all observations that were not performed in-house (i.e. subcontracted out).

Additionally, as our cut-off period of interest for data collection was determined to be December 17, several of LS 2’s conservancy project sites as at that date were still in continuation. We decided to account for this by introducing an explanatory variable: no_of_months_completed, which provides the number of months underwent for all observations.

The subsequent distribution of the above variables introduced are represented as shown:

In addition, from our data preparation phase, we remarked that in general, conservancy contracts specify the minimum number of equipment they require LS 2 to deploy for the projects. We decided to account for this in our model that specifically analyse whether an increase in any of the explanatory variables identified (and introduced) has an impact on equipment costs.   This was done by introducing three explanatory variables: minimum_battery_operated_cart, minimum_high_pressure_washer, minimum_hot_high_pressure_washer. From inspecting the table of datasets of ‘Tab 1: List of inspection unit’ prepared in ‘Facility Details (Conservancy)’, we selected these column names and screened the data by performing exploration for missing values. This was due to a few conservancy contracts not specifying the minimum number of equipment required to be deployed. Thereafter, the missing values were replaced via multivariate normal imputation, using the least squares prediction from the non-missing variables in each row.

The subsequent distribution of the above variables introduced are represented as shown:

Regression Analysis

The explanatory model being built will analyse for each major cost component, whether an increase in any of the explanatory variables determined has an impact on: (i) total project cost, (ii) manpower headcount per month as a cost driver, (iii) chemical & materials costs as a cost component, (iv) equipment costs as a cost component. Before performing regression analysis, we looked at pairwise correlations among the explanatory variables determined. This is to check whether a high linear dependency exists among pairs of predictors. The subsequent correlation coefficients across explanatory variables determined are represented as shown in the table below Thereafter, using SAS JMP we constructed the multiple linear regression model via standard least squares method that minimises the sum of squared errors. Effect screening was performed to verify the significance of each explanatory variable. Using the p-value of t-test as a rule of thumb in assessing the statistical significance of the explanatory variables, variables with p-value >= 0.05 (denote that the variable is insignificant in the model, at a 5% significance level) are removed one-by-one via backward elimination. We also check for presence of multicollinearity , and variables with high VIFs detected (VIF > 10) are subsequently removed. The model is re-computed each time to arrive at a final equation. The results of the regression model are shown in Table 2 represented below.

The table presents the results of regression analysis performed where the dependent variable is in the columns from (i) to (iv). Root mean square errors are reported in brackets.

Next, we reviewed the overall model significance to ensure goodness of fit. Using the p-value of f-test as a rule of thumb in assessing the overall fit of the regression model, a p-value of <0.05 indicates the model is significant (at a 5% significance level) in predicting the dependent variable better than its mean value. Model (i), (ii), (iii) and (iv) were ascertained to have p-values <0.05. Finally, we verified that the assumptions in multiple linear regression were respected by using the residuals plot to ensure that the errors are randomly distributed. The subsequent residuals vs. predicted value plot for model (i), (ii), (iii) and (iv) are represented as shown: