Overview In each module, you will be learning about different statistical functions in R. You will apply these functions to spec
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 models, reporting and interpreting their statistics, evaluating their significance, and using the models 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 second order regression model that contains quantitative and qualitative variables. Then you will be asked to create your own second order regression models and write a mini-report based on your findings.
- Access the R scripts for this problem set by using the Jupyter Notebook link in Module Three. In your Jupyter Notebook, you have been given a set of steps that explains how to create second order models with quantitative and qualitative variables. 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.
- Review the Module Three 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 models specified in your problem set report. Refer to the scripts that you were given as examples to guide your work.
- 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.
- Correlation Analysis: Discuss the relationships between the variables using correlation coefficients.
- 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 and constructing prediction intervals and confidence intervals.
- 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. Review the Jupyter Notebook in Codio Tutorial to help you with this task.
MAT 303 Module Three Problem Set Report
Second Order Models
[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. Quadratic (Second Order) Model with One Quantitative Variable
Correlation Analysis
Visualize and describe the relationships between the variables in the data set. Address the following question in your analysis:
· Create a scatterplot of wage growth and inflation. Comment on the relationship observed from the graph. Do you think a first order or a second order model is appropriate in this case? Explain your reasoning.
Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.
Reporting Results
Report the results of the regression model. Address the following questions in your analysis:
· Write the general form of the second-order regression model for wage growth using inflation as the predictor variable.
· Create this second-order regression model for wage growth using inflation as the independent variable. Write the model equation.
· What are the values of (R-squared) and
(Adjusted R-squared) for the model? Provide your interpretation of these statistics.
· Interpret the beta estimates for the terms inflation and inflation2 (inflation squared).
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:
· Is the model significant at a 5% level of significance? Carry out the overall F-test by identifying the null hypothesis, the alternative hypothesis, the P-value, and the conclusion of the test.
· Which terms are significant in the model based on individual T-tests? Use a 5% level of significance.
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 predicted wage growth if inflation is 7.41?
· What is the 95% prediction interval for the wage growth? Interpret the interval.
· What is the 95% confidence interval for the wage growth? Interpret the interval.
Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.
4. Complete Second Order Model with Two Quantitative Variables
Reporting Results
Report the results of the regression model. Address the following questions in your analysis:
· Write the general form of the complete second order regression model for wage growth as the response variable, and inflation and GDP growth as predictor variables.
· Create this second order regression model for wage growth as the response variable, and inflation and GDP growth as predictor variables. Write the model equation.
· What are the values of (R-squared) and
(Adjusted R-squared) for the model? Provide your interpretation of these statistics.
· Interpret the beta estimates for GDP2 (GDP squared) and inflation2 (inflation squared).
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:
· Is the model significant at a 5% level of significance? Carry out the overall F-test by identifying the null hypothesis, the alternative hypothesis, the P-value, and the conclusion of the test.
· Which terms are significant in the model based on individual T-tests? Use a 5% level of significance.
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 predicted wage growth if inflation is 7.41 and GDP growth is 9.59?
· What is the 95% prediction interval for the wage growth? Interpret the interval.
· What is the 95% confidence interval for the wage growth? Interpret the interval.
Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.
5. Complete Second Order Model with One Quantitative and One Qualitative Variable
Reporting Results
Report the results of the regression model. Address the following questions in your analysis:
· Write the general form of the complete second order regression model for wage growth using inflation and economy as predictor variables.
· Create this second order regression model for wage growth using inflation and economy as predictors. Write the model equation.
· What are the values of (R-squared) and
(Adjusted R-squared) for the model? Provide your interpretation of these statistics.
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:
· Is the model significant at a 5% level of significance? Carry out the overall F-test by identifying the null hypothesis, the alternative hypothesis, the P-value, and the conclusion of the test.
· Which terms are significant in the model based on individual T-tests? Use a 5% level of significance.
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 predicted wage growth if inflation is 7.41 and the economy is not in recession?
· What is the 95% prediction interval for the wage growth? Interpret the interval.
· What is the 95% confidence interval for the wage growth? Interpret the interval.
· Why is the prediction interval wider than the confidence interval?
Answer the questions in a paragraph response. Remove all questions and this note before submitting! Do not include R code in your report.
6. 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.
7. 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.
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