Analysis and Findings as of Finals

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Mid-Term	Finals

Derived Variables

As from the Data Exploration phase up till Mid-Terms, our team has realized that there are numerous factors that will possibly each of the different events. Therefore, our team has decided to put forward the factors, as shown in the table below, which will be used to assist us in building predictive models to explain the variations in the demands or tickets sold for each event.

No.	Factors	Description
1	Concurrent Events	Our team is hypothesizing that the events, which started at the same time period will make people buy less tickets. There might be a possibility that if there are more concurrent events ongoing, the demand may be split across the concurrent events.
2	Day of Week	The day of the week will also potentially affect the demands for each event, as events which are held in the weekdays may be attract less customers than events held over the weekends.
3	Event Name	As from our Exploratory Analysis, we realized that each of the events perform differently, and there are a multitude of factors which affects its variations in demands.
4	Time Period	Our team chose to divide 24-hours in a single day to 3-hours time block (e.g., 12AM to 2:59AM as Early Midnight & 3AM to 5:59AM as Late Midnight), as different customers might prefer events due to their lifestyle.
5	Month	The month factor is important as there might be a possibility that certain months, such as the holiday or festive season, which will potentially attract more customers to buy tickets for the different events.

With all the identified factors, our team prepared the data to be in a suitable data structure to be fed into our predictive model in the Model Calibration and Validation phase.

Model Calibration & Validation

In this phase, our team has identified 4 different models, and the aim of this phase is to calibrate the identified models based on the above derived variables and evaluate its performance through the Root Mean Square Error (RMSE).

The list below shows the 4 different models identified:

1. Regression Model
2. Decision Tree Model
3. Boosted Tree Model
4. Bootstrap Forest Model

Out of the 4 models above, all the models other than Regression Model are classified as eager learners. Since there is no provision of train and test datasets, our team will need to craft our own datasets with the following proportions as shown below:

Dataset	Proportion
Train Data	50%
Validation Data	20%
Test Data	30%

• Regression Model

The Regression Model allows us to explore and understand the relationship between a dependent variable (in our case, this is the tickets sold) and one or more independent variables (in this case, this is the derived variables in the previous subsection).

Prior to the calibration of the model, our team has decided to log-transform the number of tickets sold to assume a normal distribution, so that our model will not be dominated by extreme values.

As from the model calibrated based on the derived variables, our team managed to achieve a decent result as shown in the table below.

Dataset	R-Square	RMSE
Train Data	0.747	0.213
Validation Data	0.742	0.214
Test Data	0.746	0.211

As from the results generated from the model, it shows a decent R-Square value at approximately 0.74, and comparing the R-Square and RMSE value across all the 3 datasets, it shows that there are very signs of over-fitting and under-fitting.

And looking at the Effects Summary of the model, as shown above, it further shows that almost all of the variables played a significant amount of influence, except for the "Day" variable. Next, our team performed a step-wise regression analysis, which is an effective approach in selecting variables to be used in the model and this can help us to improve our model performance.

The following images document the process of performing stepwise-regression analysis.

• Decision Tree Model

Dataset	R-Square	RMSE
Train Data	0.813	4691.75
Validation Data	0.775	5094.41
Test Data	0.783	5003.52

• Boosted Tree Model

Dataset	R-Square	RMSE
Train Data	0.864	4000.27
Validation Data	0.810	4673.70
Test Data	0.814	4625.73

• Bootstrap Forest Model

Dataset	R-Square	RMSE
Train Data	0.818	4629.6
Validation Data	0.771	5135.6
Test Data	0.802	4774.6