Contents

Classifying MBA Student Success Risk

The MBA program staff has observed that students who are admitted to the program with a low GPA or GMAT score will often have difficulty completing the program. Students who do not complete the program or have difficulty degrades the reputation of the program. In an effort to guide admission decisions in regard to questionable GPA and GMAT scores, the staff needs a way to rate the students into three risk groups – group 1 is “low risk” and group 2 “med risk” group 3 “high risk.”

The file MBAStudents.xlsm has the data.

Learning Objectives

• To utilize Excel and R to take the data, categorize, and create cluster charts that will show a clearer visual which can assist in the decision making process.

Suggested Tools

• Excel
• R

  Statistics To Consider

• Max/Min Analysis
• Data Tables
• Cluster Chart
• k-means

  Data Source

  MBAStudents.xlsm

Tasks

Answer the questions below. Use the 6 steps of the business analytics process as a framework for completing the tasks and then write a report to make your financial decision and reasoning.

Step 1. Recognizing the problem

• What data is involved?
• What are the limitations of the data?
• How would you classify the data?

Step 2. Defining the problem

• State assumptions: The relationship between MBA admissions decisions for GPA and GMAT scores
• Are there absolute acceptances and denials based solely on score?
• Make questions that could explain the potential results from the three groupings and the area by the threshold where additional consideration should be given to those students on the borderline of the groupings.
• What would sufficient answers look like?

Step 3. Structuring the problem

• What are the admission guidelines suggested by the results?
• Should a standard be set for minimum GPA and GMAT required for admissions?
• What are our constraints?

Step 4. Analyzing the problem

• What models and techniques are needed to address the questions?
• How much confidence should you have in the results?
• How will they affect our models?

Step 5. Interpreting Results and Making a Decision

• How confident can we be in our results?
• What assumptions were made and how do they affect these results?
• What decisions can we make based off the results?

Step 6. Implementing the solution

• How would you classify the data into the different variable groups?
• What is your basis from your results of this case?
• What resources or limitations do we need to consider?

Questions to Answer

1. Create a scatterplot of GPA and GMAT scores with different colors for the “satisfactory” and “unsatisfactory” ratings of current and 90% confidence ellipses for these two groups.

2. Use k-means with 3 groups to determine the candidate clusters.

3. Assign the current students to the clusters and interpret to what degree the three clusters are meaningful.

4. Use a classification methods to determine a classification rule for the clusters.

5. Change the number of groups or using a semi-supervised approach or a different clustering method (e.g. hierarchical) and determine which causes the largest improvement.

Report

Write a professional report, as if you were a hired consultant, for the admissions director. The report should be to the point and give specific, actionable advice or solutions based on the data and analytics. Avoid technical aspects and terms that are non-essential and any speculations not substantiated by the data. This report should be concise, without lengthy explanations being necessary to understand it.

There is no minimum or maximum page limit as charts and tables can take up a highly variable amount of space. However, any charts or tables included need to be understandable to a layman at first glance. The particular models you use, interpretations, and advice given are your choice and you should be prepared to explain or defend this if needed!

Use this as an outline for the report:

A. Description of the business problem

• Background Knowledge: From the past years, what percentage of successful candidates meet the adequate GPA and GMAT scores suggested for each threshold? (Successful meaning those who finish the program or those who claim to have less difficulty)
• What are the thresholds for each of the individual three groupings? Indicate specifically what the GPA and GMAT scores are.
• What are the overall goals, objectives and drivers for these decisions?
• What are the important factors to consider for making the decisions?
• What questions will be answered and how do these explicitly help address the decisions?

B. Data, methods, and models and results

• At a high-level, discuss the basic approach, analytics used, and data and any concerns about the integrity and quality of the data used. For example, “For students who are borderline on the thresholds for the given groupings, additional consideration should be given in the case where they could have been placed in a different category based on rounding errors, etc.”

• Describe the models used (put the formula, tables, graphs, etc. here) indicating what they are used for (do not detail how they were developed or any technical details) e.g. “This chart focuses on the GPA portion of the data displaying the clusters of students and where the average GPA lies. This addresses the first factor of consideration being their GPA and in a case, where the student has a low GPA but high GMAT, this should also be brought to attention and further investigated.”

• Provide detailed answers and a rounded to the decision questions using the models
• Indicate all “important” assumptions made and why you think they are reasonable.

An assumption is important:

If you don’t make it you cannot get a result e.g. “This set of data is solely based on an unweighted 4.0 GPA scale, for example, if one obtains an A+, it will still be a 4.0 rather than a 4.3 etc.”

If the assumption is wrong or invalid your results would significantly be affected. For example, the assumption “A student with a 3.5 GPA, and a scaled score of at least 550 should be automatically accepted into the program.”

If wrong or invalid then it would significantly affect which students are accepted or denied and as a result, the program’s reputation may be further tarnished or perceived incorrectly.

Do not list technical assumptions used for statistical analysis e.g. “We assume the combination of GPA and GMAT scores are normally distributed.”

C. Decision Making

• Explain specifically how the models and results are used to make the decisions indicated in Section I. This may be literal results such as “Always accept students with a 3.8 or higher GPA regardless of their GMAT scores or vice versa (in regard to a highly scaled GMAT score e.g. 700 and above). Do not accept GPA scores lower than a 3.0 or a GMAT score lower than 550. These requirements are made due to the analyses of averages and it will further establish the more successful students who are more fit to complete the program.”

• Detail special considerations or issues to watch out for e.g. “For those that are borderline low-risk and on medium risk, they should be evaluated individually to determine the external factors that could affect their admission.”

• Describe how the improvements or benefits from using the results for making the decisions can be measured or observed. i.e. How will the admissions department determine if this process is more effective than their group meetings going through the submissions case by case? Will they save more time and money if they implement this system to assist with the admissions process and what could be a potential oversight in this process? Will there be more complaints about the process being unjust or unfair or will this system make the acceptance or denial decision unanimous among all board members?