See attached files…

Overview

In each module, you will be learning about different statistical functions in R. You will apply these functions to specific data sets, creating models that can be used to understand and solve real-world problems. You will gain practice creating a model, reporting and interpreting its statistics, evaluating its significance, and using it to make predictions.

Note: Begin working on the readings and the problem set early each week. This will help make sure that you are prepared for the weekly discussion.

Prompt

In this activity, you will explore a logistic regression model that has been created for you. Then you will be asked to create your own logistic regression models, and write a mini-report based on your findings.

1. Access the R scripts for this problem set by using the Jupyter Notebook link in Module Five. In your Jupyter Notebook, you have been given a set of steps that explains how to create a logistic regression model. Go through each step, examining the scripts and their output. If you are not sure how a specific script works or how to understand the output of a script, review the readings. Reach out to your instructor if you need additional help.

2. Review the 

Module Five Problem Set Report template

 to understand the questions that you will need to answer for this assignment. Then, write your own scripts to create the logistic regression models described in the report. Refer to the scripts that you were given as examples to guide your work.

3. Use the outputs of your scripts to answer all of the questions in your problem set report. The report has been divided into several sections. Each section contains questions to guide your analysis. Be sure to fully answer all of the questions and complete the following sections:

· Introduction: Communicate all ideas by presenting the context of your analyses.

· Reporting Results: Report the results of the model by listing and interpreting various model statistics.

· Evaluating Model Significance: Evaluate the significance of the model by reporting parameter estimates and performing hypothesis testing for each estimate and the overall model.

· Making Predictions Using the Model: Make predictions based on the model by reporting prediction values.

· Conclusion: Communicate all ideas by summarizing and interpreting the practical implications of the results.

Guidelines for Submission

You will submit your completed problem set report as a Word document. Use 11-point Calibri font and one-inch margins. You must use the equation editor where appropriate.

You will also submit the HTML file containing the outputs of your R scripts from the Jupyter Notebook. 

MAT 303 Module Five Problem Set Report

Logistic Regression

[Your Full Name]

[Your SNHU Email]

Southern New Hampshire University

Note: Replace the bracketed text on page one (the cover page) with your personal information.

1. Introduction

Discuss the statement of the problem with regard to the statistical analyses that are being performed. Address the following questions in your analysis:

· What is the data set that you are exploring?

· How might your results be used?

· What type of analyses will you be running in this problem set?

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

2. Data Preparation

There are some important variables that you have been asked to analyze in this problem set. Identify and explain these variables. Address the following questions in your analysis:

· What are the important variables in this data set?

· How many rows and columns are present in this data set?

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

3. First Logistic Regression Model

Reporting Results

Report the results of the regression model. Address the following questions in your analysis:

· Write the general form of a logistic regression model for defaulting on credit, using credit utilization and missed payments as independent variables. Note that this general form should be written in terms of E(y) and exponents.

· Now write this model in terms of the natural log of odds to express the beta terms in linear form.

· What do the following terms, from the general form of the model above, mean in terms of an individual defaulting on their credit?

a.

b.

· Create this logistic regression model and write its equation in terms of E(y) and in terms of the natural log of odds.

· Interpret the estimated coefficient of credit utilization.

· Obtain the confusion matrix and report the counts for true positives, true negatives, false positives, and false negatives.

· Report the following:

a. Accuracy

b. Precision

c. Recall

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

Evaluating Model Significance

Evaluate model significance for the regression model. Address the following questions in your analysis:

· Perform the Hosmer-Lemeshow goodness of fit test to assess whether the model is appropriate for the data set. Identify the null and alternative hypotheses, the test statistic, and the P-value. Use a

5

% level of significance.

· Which terms are significant in the model based on Wald’s test? Use a 5% level of significance.

· Obtain the Receiver Operating Characteristic (ROC) curve. Interpret the graph and explain what it illustrates.

· What is the value of AUC? Interpret what this value represents.

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

Making Predictions Using Model

Make predictions using the regression model. Address the following questions in your analysis:

· What is the probability of an individual who has a credit utilization of 32% and has missed payments in the past three months defaulting on credit? Find the odds of this event occurring. Comment on these outputs.

· What is the probability of an individual who has a credit utilization of 32% and has not missed payments in the past three months defaulting on credit? Find the odds of this event occurring. Comment on these outputs.

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

4. Second Logistic Regression Model

Reporting Results

Report the results of the regression model. Address the following questions in your analysis:

· Write the general form of a logistic regression model for defaulting on credit using credit utilization, assets, and education as independent variables. Note that this general form should be written in terms of E(y) and exponents.

· Now write this model in terms of the natural log of odds to express the beta terms in linear form.

· Create this logistic regression model and write its equation in terms of E(y) and in terms of the natural log of odds.
· Obtain the confusion matrix and report the counts for true positives, true negatives, false positives, and false negatives.
· Report the following:
a. Accuracy
b. Precision
c. Recall

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

Evaluating Model Significance

Evaluate model significance for the regression model. Address the following questions in your analysis:

· Perform the Hosmer-Lemeshow goodness of fit test to assess whether the model is appropriate for the data set. Identify the null and alternative hypotheses, the test statistic, and the P-value. Use a 5% level of significance.
· Which terms are significant in the model based on Wald’s test? Use a 5% level of significance.

· Obtain the ROC curve. Interpret the graph and explain what it illustrates.

· What is the value of AUC? Interpret what this value represents.

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

Making Predictions Using Model

Make predictions using the regression model. Address the following questions in your analysis:

· What is the probability of an individual who has a credit utilization of 43%, owns a car and a house, and has attained a high school diploma defaulting on credit? Find the odds of this event occurring. Comment on these outputs.

· What is the probability of an individual who has a credit utilization of 43%, owns a car and a house, and has attained a postgraduate degree defaulting on credit? Find the odds of this event occurring. Comment on these outputs.

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

5. Conclusion

Describe the results of the statistical analyses and address the following questions:

· Based on the analysis that you have performed and assuming that the sample size is sufficiently large, would you recommend using this model? Why or why not?

· Fully describe what these results mean in your scenario using proper statistical terms and concepts.

· What is the practical importance of the analyses that were performed?

Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.

6. Citations

You are not required to use external resources for this report. If none were used, remove this entire section. However, if you used any resources to help you with your interpretation, you must cite them. Use proper APA format for citations.

Insert references here in the following format:

Author’s Last Name, First Initial. Middle Initial. (Year of Publication). Title of book: Subtitle of book, edition. Place of Publication: Publisher.

5