Question

BUSINESS ANALYTICS

Mr. James Hatton was the proprietor of a real estate firm specializing in investment properties in the Vancouver area. Mr. Hatton’s business had done well during the real estate boom in the Vancouver area. Just recently a prospective client who held land for speculation offered Mr. Hatton exclusive listing of three properties subject to some special restrictions which the client felt would ensure that Mr. Hatton would market the properties with due diligence. The location of these properties and the prices he wished to receive were as follows:

Location Price Dunbar $200,000 Kitsilano $400,000 Point Grey $800,000

Mr. Hatton would receive a commission of 5% on any of the properties which he sold.

The client was not yet willing to offer an exclusive listing on all three properties at once. He wished first to test Mr. Hatton’s ability to sell his type of land holding. Mr. Hatton could recall almost his exact words: “But you must sell the Dunbar property first and sell it within a month. If you cannot do that I see no reason to transfer any further listings to your agency. If you do sell the property within the one month time limit, you may choose whether or not to list exclusively the Kitsilano holding for a one month period. If you are able to sell this second property within one month you will be offered the exclusive listing of the third property.” Also, for any property Mr. Hatton agrees to market, his failure to sell within a month will cancel his right to sell that property, as well as losing any options to sell other properties. Ever since this conversation, Mr. Hatton had sought to analyze this proposition. He assessed the selling costs from his previous experience in advertising and selling similar properties in the past. These costs would be incurred even if no sales were made. Of course, these costs would not be incurred if Mr. Hatton refused a listing. Mr. Hatton also assessed his chances of sale within a month based upon his historical experience with similar parcels at the same general price level. He wrote this information in a simple table for further study.

Property Promotional Expense Prob. of Sale within One Month Dunbar $8000 .6 Kitsilano $2000 .7 Point Grey $4000 .5

Part (A) Mr. Hatton was sure that the costs, expenses and probabilities associated with the sale of each of these properties were in no way dependent upon the sale or availability of the other properties. Mr. Hatton hired a recent B.Com. Graduate to perform a full analysis of his decision problem.

 Do the full decision tree analysis.

Part (B) Before Mr. Hatton had a chance to respond to the above proposal regarding the three properties, the client sold both the Dunbar and the Kitsilano properties. However, Mr. Hatton still had the option of trying to sell the Point Grey property, and the information about the Point Grey property remains the same as given in the above table. Mr. Hatton also decided to consider the possibility of doing a very quick market survey to get a better idea of the chances of a sale. The cost of such a survey would be $3000. Based upon past experience, Mr. Hatton is able to estimate that in the cases of successfully selling (within in a month) a property like the Point Grey property, there were 80% of these cases that the market survey indicated a strong real estate market, whereas in the cases of failing to sell (within in a month) a property like the Point Grey property, there were 60% of these cases that the market survey indicated a weak real estate market. Impressed with the analysis of the previous problem, Mr. Hatton asked the same B.Com. Graduate to analyze fully the new problem.

 Do the full decision tree analysis.

 What is the Expected Value of Sample Information (EVSI)?

 What is the Expected Value of Perfect Information (EVPI)

Answer the report in the form of a "Report to Management" (Header, introduction, recommendation, and data and analysis)

Answer 1

1. Decision tress often mimic the human level thinking so its so simple to understand the data and make some good interpretations.
2. Decision trees actually make you see the logic for the data to interpret(not like black box algorithms like SVM,NN,etc..)

For example : if we are classifying bank loan application for a customer, the decision tree may look like this

Here we can see the logic how it is making the decision.

It’s simple and clear.

So what is the decision tree??

A decision tree is a tree where each node represents a feature(attribute), each link(branch) represents a decision(rule) and each leaf represents an outcome(categorical or continues value).

The whole idea is to create a tree like this for the entire data and process a single outcome at every leaf(or minimize the error in every leaf).

Okay so how to build this??

There are couple of algorithms there to build a decision tree , we only talk about a few which are

1. CART (Classification and Regression Trees) → uses Gini Index(Classification) as metric.
2. ID3 (Iterative Dichotomiser 3) → uses Entropy function and Information gain as metrics.

Lets just first build decision tree for classification problem using above algorithms,

Classification with using the ID3 algorithm.

Let’s just take a famous dataset in the machine learning world which is weather dataset(playing game Y or N based on weather condition).

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We have four X values (outlook,temp,humidity and windy) being categorical and one y value (play Y or N) also being categorical.

so we need to learn the mapping (what machine learning always does) between X and y.

This is a binary classification problem, lets build the tree using the ID3 algorithm

To create a tree, we need to have a root node first and we know that nodes are features/attributes(outlook,temp,humidity and windy),

so which one do we need to pick first??

Answer: determine the attribute that best classifies the training data; use this attribute at the root of the tree. Repeat this process at for each branch.

This means we are performing top-down, greedy search through the space of possible decision trees.

okay so how do we choose the best attribute?

Answer: use the attribute with the highest information gain in ID3

In order to define information gain precisely, we begin by defining a measure commonly used in information theory, called entropy that characterizes the (im)purity of an arbitrary collection of examples.”

wikipedia

For a binary classification problem

• If all examples are positive or all are negative then entropy will be zero i.e, low.
• If half of the examples are of positive class and half are of negative class then entropy is one i.e, high.

Okay lets apply these metrics to our dataset to split the data(getting the root node)

Steps:

1.compute the entropy for data-set

2.for every attribute/feature:
       1.calculate entropy for all categorical values
       2.take average information entropy for the current attribute
       3.calculate gain for the current attribute

3. pick the highest gain attribute.
4. Repeat until we get the tree we desired.