Statistical Research Projects
Project Objective: Application of statistical concepts and techniques taught in QM 292.
Project Outcomes: Formulation of research hypothesis and relevant model specification, data set construction, and empirical analysis of model results.
Students can work as individuals or in teams of two. The project consists of 5 phases with each phase due to the instructor by midnight of the prescribed due date. Each completed Phase must be submitted to me in Canvas by the due date. The project is worth 100 points and constitutes 10% of your total grade for this course.
Failure to submit a completed phase by the due date will result in a penalty of 10 points for each late phase.
Note of caution, if you choose to work in a team and your team member fails to submit an individual phase by the due date or submit the project in its entirety by the due date, both team members will be assessed penalty points. If your team member withdraws from the course, you alone will be responsible for the project which includes meeting all required deadline submissions.
Graduating seniors who fail to submit the final project as an individual or as part of a team will receive an I (incomplete for the course).
Each project phase (1-5) must be submitted to the instructor through Canvas.
The project is due May 1, 2021 in electronic format. Submit the assignment from within the Canvas Assignment.
PHASE 1 March 24, 2021
a. Identify and state a research question of interest. The research question must be stated such that multiple linear regression can be applied to the analysis of the question. In Phase 1 address (a) why is your research question of interest to the reader and (b) Why is your research question relevant?
Examples of questions where multiple linear regression is not applicable:
a. Is there any difference in BMI between males and females? This is test of means.
b. Does Google stock have greater performance variability as compared to Yahoo? This is a variance test.
Examples of research questions might be:
c. Females or more likely to attrite from college then males. Alternatively, this can be phrased as Is there any difference in the college attrition rate between the genders?
d. Is the consumer price index a good predictor of Christmas retail spending?
e. Was President Obamas American Recovery and Reinvestment Act successful in stimulating the US economy after the May 2007 housing crash?
f. What factors are most likely to influence stock performance?
g. Does parental income and education influence BMI?
h. What factors contribute to US city homicide rates?
i. To what extent is defense spending influenced by world oil prices and US oil demand?
j. What factors (demographic, macroeconomic, industrial spending, environmental) are most likely to predict the outbreak of Ebola or other diseases (polio, malaria, bird flu)?
PHASE 2: Model Statement April 6, 2021
2. In a general format, state the model. In other words, identify your dependent and independent variables. Your model must include at least 3 independent variables, but not to exceed 7 independent variables.
a. EXAMPLE: If your research question is: Does parental income and education influence BMI? , then the dependent variable would be BMI and the independent variables would be parental education and parental income.
i. The general model statement: BMI = f(parental education, parental income).
2b. Identify the source or sources of your data. When using cross-sectional data ALL data must be pulled from the same time period but can be pulled from different sources. Identify the source and time period for each data element.
2c. Data sets much have a minimum of 50 observations, but not to exceed 100 observations.
2d. Include a definition of each data element, data source, and period for which data element is captured.
For example: BMI = Body Mass Index, is measure by body mass divided by the square of the individuals height. Data source: Health and Human Services, www.hhs.gov, fiscal year 2010, state level data.
Example #2: Parental income = is combined household annual income as measured in thousands of US dollars. Data Source: www.bls.gov, state level data for 2012.
IMPORTANT: Your dependent variable cannot be binary, categorical/ranking, or strictly a discrete variable. Your dependent variable must be a continuous variable. Your independent variables can be all continuous or a mix of discrete and continuous. Your independent variables CANNOT be strictly discrete variables.
Submission of Phases I II: Must be submitted in WORD format. As part of the Phase II submission include Phase I so that the grader can follow the flow of ideas. Definition of variables (see Phase II 2b) should include time period data is captured, explicit definition of variable measurement or how the variable will be transformed for inclusion in Phase IV. For example:
INCORRECT: Weight how much a person weighs.
CORRECT: Weight weight as measured in pounds, data source Center for Disease Control, www.cdc.gov, individual level data, 2010.
INCORRECT: Unemployment rate the unemployment rate
CORRECT: Unemployment rate the number of people unemployed per 1000, data source Bureau of Labor Statistics, www.bls.gov, state level data 2011.
Footnote:. You don’t need to exactly specify your transformation steps at this point, but at least discuss the type of variable and your guesses about what kind of transformation may be necessary. We will get into the specifics of the transformations in the next phase. However, this is a ‘look ahead note’ on the Transformation of Categorical Variables: Categorical variables such as gender, race, color, manufacturing sector, team, geographic region, as examples, need to be transformed into quantitative variables. For example, gender is captured as M or F, this will need to be transformed into 0,1 variable.
Example: M = 0 and F = 1 or M =1 and F = 0. The definition should read if M then M = 0 and if F then F=1
Example: Lets assume your data contains 4 geographic regions, North, South, East, and West then for Phase II you will need to define the states that comprise the North geographic region, similarly for east, west, and south. In Phase III, you will need to transform these variables into columns of 0,1 dummy variables.
PHASE 3: Data Collection April 13, 2021
3. Analysis of your research question requires data. There are three general sources of data; (1) survey, (2) historical data, and (3) experimental data. For purposes of this course students are limited to public use data, (i.e. data available on the world wide web).
a. Historical data is largely collected by public and private institutions. There are numerous publicly available data sources on the web:
i. https://www.who.int/healthinfo/statistics/en/
ii. http://www.bls.gov/data/
iii. http://www.freefinancialdata.com/stocks/index-data/
iv. http://www.census.gov/compendia/statab/
v. http://www.healthdata.gov/
vi. http://nces.ed.gov/
vii. www.city-data.com
viii. http://statsamerica.org/
b. Other data sources can be found by doing a google search. For example, a google search on carbon emissions data yields the following data https://en.wikipedia.org/wiki/List_of_countries_by_carbon_dioxide_emissions
c. Students may NOT USE data from the following sources: Zillow, realtor.com, carmax.com, or ESPN. Students are permitted to choose research topics on housing, vehicles, and athletes but MUST use other data sources.
Identify your data source(s). Once the data source(s) has/have been identified, input the data into an excel spreadsheet. Your data set must contain minimum of 50 observations. All data must be cross sectional data. Cross sectional data is defined as different observations within the same time period. Examples of an excel data set is provided below:
Example 1
Example 2
Submission of Phase III: Phase III must be submitted in EXCEL format. Attach Phase I-II in your submission. This allows me to verify the accuracy of your data and data format in terms of your Phase I-II statements and definitions. See examples provided earlier in the document as to how your data should be captured.
Excel CANNOT read alpha characters. All alpha characters must be transformed into 0,1 variables. See examples below.
Transformation of variables – geographic example provided above:
Geographic Region North East West South
N 1 0 0 0
N 1 0 0 0
W 0 0 1 0
E 0 1 0 0
S 0 0 0 1
S 0 0 0 1
E 0 1 0 0
Transformation Example: For Individual level Race Variable
Race White African American Hispanic Asian
White 1 0 0 0
White 1 0 0 0
Asian 0 0 0 1
African American 0 1 0 0
Hispanic 0 0 1 0
African American 0 1 0 0
White 1 0 0 0
Transformation Example: Individual Level Gender Variable
Gender Gender Binary m= 1 f = 0
M 1
F 0
F 0
M 1
Transformation Example: National Football Conference American and National League
League American = 1 National = 0
American 1
National 0
American 1
American 1
PHASE 4 Regression Output April 22, 2021
4. Using excel Data Analysis Toolpak run your regression. Save your output to a separate spreadsheet. A tutorial for this add-in can be found at http://cameron.econ.ucdavis.edu/excel/ex61multipleregression.html
Submission of Phase IV Phase IV must be submitted in EXCEL format. Include in your submission Phase I-III in the format discussed above. There is a high probability that your initial regression outputs will be incorrect or explode. Indications that your regression output is incorrect include:
a. Blank cells in the output
b. Observe NUM in a cell
c. Very high R-squared
d. Negative R-squared
e. R-squared that exceeds 1
f. Excel error message that the data is not compatible
If you should encounter these problems, check the following:
1. Cells do NOT contain formulas.
2. Cells do not contain alpha characters, spaces, blank cells, or other non-numeric values.
3. Dummy variables are correctly captured.
4. That the sum or difference of any two columns does not equal a third column
5. In the case of dummy variables, you must drop (do not include) at least 1 of the dummies.
I will review each regression model for accuracy. I strongly encourage you to run your regressions as soon as possible. In other words, I would not recommend waiting until the due date to run your regressions.
PHASE 5 Due May 1, 2021. PHASE 5 will not be accepted late see syllabus.
5. Report your findings/results from the regression analysis. Project report should not exceed 8 pages EXCLUDING appendices, can be single or doubled space, and must be in Times New Roman, 12 point font, 1 inch margins formats. You must be sure to follow the outline below and address all questions, discuss all metrics, output, findings, and conclusion as outline below. Final reports will include Phase I-IV information and for Phase V need to discuss/include the following:
Final Report Format and Contents
READ THE INSTRUCTIONS CAREFULLY
Follow the outline as exactly detailed below. Address each section and address the content under each section. Failure to follow the outline or address the content of each section will result in points deducted.
Papers are to be submitted in well written English, grammatically correct, and in complete sentences.
Papers must be submitted DOUBLE SPACED, 11 or 12 point font, 8 Page limit NOT including appendices or references.
Papers MUST be submitted in format specified, labeled, and addressing points discussed below.
Phase 5 Research Paper Outline:
1. Cover page including title of project, your name, date, and an abstract. Abstract should not exceed 3 paragraphs.
b. NOT INCLUDED IN 8 page limit
2. Introduction in well written English, discuss Phase I and Phase II part 2b.
a. Why is your research question of interest? Why is it relevant?
3. Data Section discuss your data, data definitions, any transformations, data source, data time period this section references Phase II part 2b and Phase III.
a. DO NOT include a copy of your data tables in the body of the paper. You may include a copy of the data table in the Appendix but this is optional.
4. Regression Output (Phase IV) – In this section discusses any modifications to the original model statement specified in Phase II. For example, deletion of variables, alternative specification of the original model statement ect.
a. Your regression output is part of the appendix and NOT part of the main paper.
5. Results
a. Discuss how your regression results do or do not support Research questions/hypothesis.
b. Using relevant test statistics (listed below) discussion of findings. Does the data support your research question/hypothesis?
i. F-Test – discuss the test metric including purpose (what is it testing), results, decision/conclusion as it relates to your research question.
ii. R-squared discuss the test metric including purpose (what is it testing), results, decision/conclusion as it relates to your research question.
iii. Statistical significance based on t-test – discuss the test metric including purpose (what is it testing), results, decision/conclusion as it relates to your research question.
iv. Marginal effects – Using the data and coefficients, provide examples of and discuss marginal effects. In cases where the coefficients are (a) discrete or (b) statistically insignificant discuss the limitations of computing marginal effects.
v. Prediction using your regression output, provide an example of model prediction. In other words, chose values within the range of your independent variables, compute the predicted value, and discuss this prediction in light of your research hypothesis.
c. Conclusion summarize empirical results, how do the regression findings do or do not support your hypothesis, discuss shortcomings of the model, how would you improve model, and ideas for future research.
Appendices (NOT INCLUDED IN 8 PAGE LIMIT):
a. Appendix A: For each variable in your data set provide descriptive statistics. Discuss 2-3 of the variable summary/descriptive statistics. For example, if the average value of a variable in your data set differs from National or State level means, large variances, non-normal distributions ect.
b. Appendix B: Include table of regression results.
c. Appendix C: Copy of original data optional
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