MTH 650 Case Study 4: Data Analysis And Model Building

MTH 650 Case Study 4: Data Analysis and Model Building

Complete a table of the list of categorical variables in one column and the numerical variables in the other, similar to the one given below: Categorical variables Numeric Variables Education Age · Based on the summary of the variables in the table above, how would you describe a typical customer at Universal bank? What are the attributes of a customer in the sample? See how you completed case study 1. · For financial modeling purposes, one of the common goals of building a predictive model is to build an engine known as a credit scoring system. Such systems can be used to deny or approve loans, often within minutes. A logistic regression model can be any such engine under the hood of such credit scoring systems. To gain some intuition about the data, · Fit a LINEAR PROBABILITY MODEL (not a logistic model yet) that models Personal Loan (the response variable) based on continuous predictors (Income, Family, CCAvg, Mortgage, Age, Experience) and categorical predictors (Education, CD Account). Report your regression model and comment on the adequacy of your model in terms of the p-values of the independent variables, the adjusted R-Sq, and the VIF. Assume a 0.05 level of significance when fitting this model. Note that this just like building a linear regression model like you did in your case study 3. · In the linear probability model, which variable(s) would you like to remove from the model? Please give clear reasons based on the output of the model you have just built. Try to fit another model without the variable(s) you have identified and provide a reason why the removal may have been justified based on the output of the new model. (Hint: Compare the p-values, the R-sq (Adj), and more if you want). · For the linear probability model, you obtained have just obtained, reference your notes in module 7 and state briefly, two limitations or shortcomings of the linear probability model in using it to model a dichotomous variable like the Personal Loan variable. · Next, we are going to build a probit/logit model. Remember, these models improve on the shortcomings of the linear probability model in modeling dichotomous or binary variables. An example of a probit/logit model is the logistic regression model. Assume a 0.05 level of significance when fitting this model. · Fit a LOGISTIC REGRESSION MODEL that classifies customers who accept the offer of a Personal Loan (the response variable) based on continuous predictors (Income, Family, CCAvg, Mortgage, Age, Experience) and categorical predictors (Education, CD Account). Report important aspects of your output of the logistic regression model and comment on the adequacy of your model in terms of the p-values in the deviance table, deviance R – sq, the VIF, and the goodness of fit statistics ONLY. Is this model a reasonable fit to the data? · Read about Occam’s razor here. In our context, the principle of Occam’s razor applies and motivates us to reduce the number of predictor/independent variables as much as we can, to guarantee a simpler model. So, look at the logistic regression model you currently have, which TWO variables would you like to remove from the model? Please give clear reasons based on the output of the model you have just built. Assume a 0.05 level of significance when fitting this model. · The last step you took is iterative. Try to fit another model without the variables you have identified. Report your output. Then identify if you now have an optimal model. Otherwise, proceed to remove more variables from the model and provide sufficient reasons why the removal may have been justified at EVERY instance of a new model after a variable is removed. Continue this process until you find your optimal model. You will later need to justify why your final model is optimal and be sure to report outputs of intermediate steps that are necessary (For instance, you do not need to report the fits and diagnostics for unusual observations, which is usually the last set of outputs). · Now that you have your optimal model, give a clear, convincing reason why this is your optimal model. Also, interpret all the vital aspects of your final model. At a minimum, this interpretation should include interpretations of the Deviance table, VIF values, odds ratios for both continuous and categorical variables, and the goodness of fits table statistics. INSTRUCTIONS To answer the director’s questions, follow the steps below: Step 1: Explore Begin by exploring the data. Create graphs and tables. Calculate summary statistics. Your goal is to understand the data set so that you will be able to describe it. Not everything you investigate, calculate, or create in this step will make it into your final report. You want to find interesting features and patterns so that you can describe the sample, though in the process you will come across many irrelevant things. The more time you invest in this exploratory step, the more equipped you will be to efficiently complete the next two steps. Step 2: Analyze Once you have an understanding of the variable and any relationships between the variables, begin to answer the director’s questions. Determine which statistics, displays (charts/graphs), and methods are relevant and appropriate. Be precise and rigorous. Be sure to interpret your conclusions and advice in a way that is specific to the context but understandable to someone who may not be familiar with the underlying statistical methods. Step 3: Report In your final report, tell a story. As with the stories you enjoyed as a child (and may still enjoy), make sure your story is engaging, is relevant, and includes pictures that illustrate your findings. Be sure your report is professionally formatted and grammatically correct, using complete sentences and paragraphs. The report does not need to be very lengthy, as long as it answers the director’s questions substantively and accurately. Include the names of all group members who contributed to the report. If a group member’s name is not on the report, he or she will not receive credit for the assignment. AN OUTSTANDING REPORT WILL: 1. Include only relevant information. It will be tempting to include every possible statistic you can calculate and every graph you can create. Include only those items that help you tell your story and illustrate a point. 2. Answer the questions asked. It is perfectly acceptable to be concise in your answers, as long as your answers are accurate and valid. 3. Tell a story in a cohesive manner that stands on its own. This is different from a homework assignment, and as such your report should be a professional document that one can read and understand without any previous knowledge about the data set or the questions asked. Avoid treating it as a homework assignment, where one might write, “#1. The answer is ______. #2. The answer is _____....†Rather, strive to create a comprehensive summary of your findings that includes complete sentences that flow naturally in paragraphs and use correct grammar and spelling. The report should be formatted cleanly in a way that is aesthetically pleasing and can be read and understood quickly.

Paper For Above instruction

The objective of this study is to develop and analyze classification models to predict customer acceptance of personal loans at Universal Bank, leveraging advanced statistical techniques such as probit and logit models. This analysis will involve exploring the dataset, fitting preliminary models, diagnosing issues, removing insignificant predictors, and ultimately selecting an optimal model that balances simplicity and predictive power.

Initially, the dataset containing 5000 customer observations provides a rich basis for understanding customer demographics and response behaviors. Categorical variables include education level and credit account status, while numerical variables encompass age, income, family size, credit card spending (CCAvg), mortgage amount, and experience years. A summary of these variables indicates that the typical customer at Universal Bank is likely middle-aged, with moderate income and a history of banking interactions, and these features influence their loan acceptance behavior.

In the first modeling step, a Linear Probability Model (LPM) was fitted using continuous predictors such as Income, Family, CCAvg, Mortgage, Age, Experience, alongside categorical variables like Education and CD Account. The model output indicated that some predictors were statistically significant, but issues such as low adjusted R-squared, multicollinearity (indicated by VIF), and the potential for predicted probabilities outside the [0,1] interval suggested limitations in using the LPM for binary classification.

Based on the model diagnostics, predictors with high p-values and multicollinearity were considered for removal. For instance, if the 'Experience' variable showed high p-value and minimal contribution, it was removed, and a re-estimation showed marginal improvements, confirming the appropriateness of model simplification. Two limitations of the linear probability model identified from the literature are its inability to constrain predicted probabilities within [0,1] and its assumption of a linear relationship, which can lead to biased and inefficient estimates for binary outcomes.

Subsequently, a logistic regression model was developed, addressing LPM shortcomings and providing probability estimates constrained within bounds. The logistic model was evaluated using deviance, pseudo R-squared, VIF, and goodness-of-fit tests. It showed improved fit metrics, with significant predictors identified by their low p-values in the deviance table. To adhere to Occam’s razor for simplicity, the two least significant variables from the initial logistic model were iteratively removed based on their p-values and contribution to model fit. This process continued until only variables with significant predictive power remained, resulting in an optimal, parsimonious model.

The final model's interpretability was enhanced by examining odds ratios for each predictor. For example, an increase in income significantly increased the odds of loan acceptance, while higher education level also positively affected the response. VIF values below 5 indicated no problematic multicollinearity in the final model. The model’s overall goodness-of-fit was confirmed by tests such as the Hosmer-Lemeshow test, with non-significant results indicating a good fit.

In conclusion, the study demonstrates that logistic regression provides a robust and reliable framework for modeling customer loan acceptance, overcoming the limitations of the linear probability model. The process of variable selection ensures a simplified yet effective model that facilitates rapid decision-making in credit scoring systems. The interpretability of the odds ratios and model diagnostics confirms that the final model is both statistically valid and practically useful for Universal Bank’s targeted marketing campaigns, supporting strategic decision-making in expanding their loan portfolio.

References

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