Northeastern University Online College of Professional Studies Course Syllabus CED 6030 Applied Mathematics and Statistics for Economics Winter 2018, 12-week term January 8 March 31, 2018 Instructor Name: Dr. Michael P. Stone E-mail: m.stone@northeastern.edu Phone Number: (617) 373-2882 Office: Holmes Hall 305 Office Hours: TBD Lecture: Wednesday 5:50 to 8:00 Location: TBD FT Required Text(s)/Software/Tools: This course is divided into two components a statistics component, and a calculus component. There are two required textbooks and one required statistics homework package. For the statistics component of the course, the required textbook is: th RA Statistics for Business and Economics (8 ed., 2012) By Paul Newbold ISBN-10: 0132745658 ISBN-13: 9780132745659 Publisher: Pearson Math & Statistics D You are also required to purchase an access code for MyStatLab, an online program that will be utilized to complete homework assignments. Please note that an etext version of the abovementioned book is included with your purchase of MyStatLab. Once you have obtained an access code, you must register for this course in MyStatLab by inputting the following Course ID: TBD. For the calculus component of the course, the required textbook is: Calculus (1991) By Gilbert Strang Publisher: Wellesley-Cambridge Press This textbook is available on Blackboard. 1
Course Prerequisites None. Course Description Seeks to meet the practitioners' needs for applied research and analysis. Offers students an opportunity to develop and reinforce mathematics tools and basic probability, descriptive statistics, estimation techniques, statistical hypotheses, sampling, analysis of variance, correlation, and regression analysis in the context of economics. Computer applications are an integral part of the course and support theoretical and applied analysis required for professional development. Course Outcomes Students will have the opportunity to learn the basic statistical and mathematical tools used in economics. Students will analyze statistical and constrained optimization problems, both of which are routinely examined by economists. The tools discussed in this course will provide students with the opportunity to become knowledgeable and conversant in the following: Describing data in terms of measures of central tendency and variation Applying the basics of probability theory, set theory, and probability rules Distinguishing discrete from continuous data and the distributions that can be used to approximate these data Estimating measures of central tendency and variation for a population given sample data. Hypothesis testing of unknown population parameters given sample data Using methods of fitting data to a linear form Applying functional forms involving exponents and logarithms Obtaining the slope of a function via differentiation to determine rates of change Finding the maximum values and minimum values of specific functions over a given range of values Optimizing functions given external constraints Course Methodology Each week, you will be expected to: 1. Review the week's learning objectives. 2. Complete all assigned readings. 3. Complete all lecture materials for the week. 4. Participate in the Discussion Board (note: this is a biweekly requirement, with the first assignment due at the end of week 1). 5. Complete and submit all assignments and tests by their respective due dates. Participation/Discussion Board The Discussion Board is split into two sections. 1. Public (Entire Class) Section This section contains all students in our class and consists of three distinct forums: Introduce Yourself!, Ask the Instructor, and Student Networking/Watercooler. a. Introduce Yourself! Use this forum to provide a brief biography of yourself. You will find it advantageous to include a personal avatar so we can identify with one another both inside and outside of class. b. Ask the Instructor Use this forum to ask procedural and substantive questions about the course. Please create new threads pertaining to questions that arise throughout the course of the semester. Participation in this forum is not mandatory, and accordingly, your final grade will not be directly affected by activity within this forum. 2
c. Student Networking/Watercooler Use this forum to participate in a general discussion with classmates about topics that otherwise fall outside of the topics discussed in class. All posts must be professional, and obscenity/harassment will not be tolerated. Participation in this forum is also not mandatory. 2. Individual Student Group An Individual Student Group consists of all members who are working on the Final Group Project (see Appendix A) together. On the first day of class, you will choose with whom you will work to complete this project. Each Individual Student Group will consist of no more than three (3) students. Beginning week 1 and thereafter bi-weekly, I will assign each Individual Student Group a series of questions that are relevant to the Final Group Project. The student group must complete the assigned tasks prior to the submission deadline. Answers will be posted in Blackboard, and I only require one answer to each question, which will be submitted on behalf of the entire Individual Student Group. All members of a group will receive the same grade for each Discussion Board assignment. Discussion Board participation is worth 5% of your final grade. Communication/Submission of Work All homework assignments will be completed using MyStatLab. Each week, I will assign between 15 and 20 statistical and/or mathematical problems, ranging from core definitions to practical applications. You will have three (3) attempts to complete each homework assignment. I will not accept late homework assignments or hard copies of assignments in lieu of online submission. Failure to complete an assignment by its deadline results in a zero (0) for that assignment's grade. You are responsible for ensuring that your homework grades are correct in MyStatLab prior to assignment deadlines. After the submission deadline has passed, I will manually enter homework grades into the Grade Center in Blackboard. You can expect this integration to occur within 48 hours of the submission deadline. Once your assignment has been graded, you will be able to view the grade and feedback I have provided by clicking on My Grades in the Tools module from the Northeastern University Online Campus tab. Please do not hesitate to ask questions during lecture. For issues that arise outside of lecture, email me or attend my office hours. If you have a question that you feel may be shared by your colleagues, create a thread in the Entire Class forum of the Discussion Board so your colleagues may also benefit from my response. Grading/Evaluation Standards Your final grade will be based on your performance on a Midterm and Final Exam, multiple homework assignments, one-half dozen Discussion Board assignments, and a Final Group Project. An average grade in this course is a B. In computing your final grade, the following weights will be used: Midterm Exam 25% Final Exam 25% Final Group Project 25% Homework 20% Discussion Board 5% Total 100% Final grades will be assigned according to the following scale: 93% - 100% = A 80% < 83% = B- 60% < 70% = D 90% < 93% = A- 77% < 80% = C+ < 60% = F 87% < 90% = B+ 73% < 77% = C 83% < 87% = B 70% < 73% = C- As noted above, homework assignments will be completed in MyStatLab, and you will have three (3) attempts to complete each homework assignment. You will have as much time as you please to complete each homework assignment, provided submission occurs prior to the deadline. Exams will 3
consist of multiple choice and short answer problems, and they will be completed within Blackboard. These exams may be completed at any time during the exam period, but you will have only two (2) hours to complete each exam. Therefore, unlike homework assignments, you will be constrained for time and you will only have one (1) attempt to complete each exam. You must complete all assignments by their respective deadlines, and I will not accept a late submission unless you present sufficient evidence of a valid, university-recognized excuse (e.g., hospitalization, death of close family member, etc.). Please reference Appendix A for guidelines pertaining to the Final Group Project. Class Schedule / Topical Outline Note: Readings should be completed prior to onsite lecture. All assignments are due by 11:59 pm on the last date specified in the Dates column. Week Dates Topic Reading Assignments 1 1/8 1/14 Academic Integrity Policy Introduction; Describing Data Newbold Chs. 1, 2 Homework I Discussion Board I 2 1/15 1/21 Probability Theory Newbold Ch. 3 Homework II 3 1/22 1/28 4 1/29 2/4 Discrete Probability Distributions Continuous Probability Distributions Newbold Ch. 4 Newbold Ch. 5 5 2/5 2/11 Sampling Distributions Newbold Ch. 6 6 2/12 2/18 Confidence Interval Estimation Newbold Ch. 7 7 2/19 2/25 Hypothesis Testing Newbold Ch. 9 Homework III Discussion Board II Homework IV Homework V Discussion Board III Homework VI Midterm Exam Homework VII Discussion Board IV 8 2/26 3/4 Regression Analysis I Newbold Chs. 11, 12 Homework VIII 9 3/5 3/11 Regression Analysis II Newbold Ch. 13 10 3/12 3/18 Differentiation I 11 3/19 3/25 Differentiation II; Constrained Optimization Strang Ch. 2, 1-3, 5 Strang Ch. 13, 1-2 Strang Ch. 3, 2-3 Strang Ch. 1, 1-4 Strang Ch. 13, 6-7 Homework IX Discussion Board V Homework X 12 3/26 3/31 Final Group Project None Homework XI Discussion Board VI Final Exam Final Group Project The University views academic dishonesty as one of the most serious offenses that a student can commit while in college and imposes appropriate punitive sanctions on violators. Here are some examples of academic dishonesty. While this is not an all-inclusive list, we hope this will help you to understand some of the things instructors look for. The following is excerpted from the University s policy on academic integrity; the complete policy is available in the Student Handbook. The Student Handbook is available on the CPS Student Resources page > Policies and Forms. Cheating intentionally using or attempting to use unauthorized materials, information or study aids in an academic exercise 4
Fabrication intentional and unauthorized falsification, misrepresentation, or invention of any data, or citation in an academic exercise Plagiarism intentionally representing the words, ideas, or data of another as one s own in any academic exercise without providing proper citation Unauthorized collaboration instances when students submit individual academic works that are substantially similar to one another; while several students may have the same source material, the analysis, interpretation, and reporting of the data must be each individual s independent work. Participation in academically dishonest activities any action taken by a student with the intent of gaining an unfair advantage Facilitating academic dishonesty intentionally or knowingly helping or attempting to violate any provision of this policy For more information on Academic Integrity, including examples, please refer to the Student Handbook, pages 9-11. Northeastern University Online Policies and Procedures For comprehensive information please go to http://www.cps.neu.edu/online/ Northeastern University Online Copyright Statement Northeastern University Online is a registered trademark of Northeastern University. All other brand and product names are trademarks or registered trademarks of their respective companies. This course material is copyrighted and Northeastern University Online reserves all rights. No part of this publication may be reproduced, transmitted, transcribed, stored in a retrieval system, or translated into any language or computer language, in any form or by any means, electronic, mechanical, magnetic, optical, chemical, manual, or otherwise, without the express prior written permission of Northeastern University Online. Copyright 2017 by Northeastern University Online All Rights Reserved 5
Appendix A Final Group Project The objective of the Final Group Project is to properly use regression analysis to answer a question that interests you. Examples of interesting questions include: what are the determinants of the wage rate, or what are the determinants of demand for a particular product? You are granted great latitude in choosing the question you seek to answer. You will work in groups of size three (3) and all group members will receive the same grade. The students with whom you work to complete this project constitute your Individual Student Group in the Discussion Board. In ten (10) to fifteen (15) pages of double-spaced writing (Times New Roman or Arial font; 1 margins) in a Word document, each group must complete the following: 1. Describe the question that interests you and build a crude theoretical model. a. What are you trying to explain, i.e., what is the dependent variable? Why does its explanation interest you? b. What are the determinants, i.e., independent variables, that you believe explain the dependent variable? You must have at least three (3) independent variables. c. What does the previous literature have to say about your question? You do not need to fill a hole in the literature. You must cite at least three (3) reputable sources (peerreviewed articles) in this literature review. d. What are your hypotheses? Do not forget to describe the expected relationship (i.e., direct, indirect, or ambiguous) between each of the independent variables and the dependent variable. 2. Build a multiple linear regression population model. a. What is the multiple linear regression population equation? b. What are the assumptions underlying the population model? c. Are any of these assumptions likely violated? If so, why? (You simply need to recognize the potential flaws in your empirical analysis. This course will not equip you with the tools to correct these problems.) 3. Gather the appropriate data or proxies and describe these data. At a minimum, you must have at least thirty (30) observations, but if more sample data are readily available, you must include them. a. Provide a table of summary statistics, just like one would see in a scholarly article. b. At first blush, do these summary statistics somehow initially support or contradict your hypotheses? c. Use graphical depictions of data to aid the reader in visualizing trends and/or relationships. d. Identify the sources of your data (e.g., State-level population data are obtained from the Census Bureau, available at www.census.gov. ). Note that these data should be contained in a Microsoft Excel spreadsheet, and a digital file of these data must accompany your submission. 4. Using your dataset, estimate the population model, and interpret all coefficients. a. What is the marginal effect on the dependent variable of a one-unit increase in the value of each independent variable? b. Identify and interpret all confidence interval estimates. c. Identify the significance level for all coefficients. Are any estimates statistically significant? If so, at what level (i.e., 1%, 5%, or 10%)? 5. Interpret the adjusted coefficient of determination and F-statistic (including its significance). a. What portion of the variability in the dependent variable is explained by the independent variables? b. Does your model do an adequate job of explaining variation in the dependent variable? 6
6. Elaborate on your results in a discussion. a. Based on your answers above, is there empirical evidence to support your initial hypotheses? b. Are there any inconsistencies between your hypotheses and your actual results? Why do you think these inconsistencies arose? c. How does this project fit in with the pre-existing scholarly literature on the topic? d. Based on your empirical results, do you believe that your theoretical model needs revision? e. How could this project be improved in the future? 7