Brandeis University Professor Linda T.M. Bui Department of Economics Sachar 107-125, 6-4848 ltbui@brandeis.edu 83A STATISTICS AND ECONOMIC ANALYSIS FALL 2011: TENTATIVE Course Overview: This course is designed to provide a working knowledge of the analytical tools of probability and statistics used in economic analysis. Some of the topics that we will cover include descriptive statistics, probability theory, the Central Limit Theorem, confidence intervals and hypothesis testing. The course will conclude with an introduction to regression analysis using the bivariate model involving a derivation of the ordinary least squares estimators. The Gauss Markov Theorem will be introduced and proved. Course Meeting Times: Section 1: MWTh 10:00 a.m. - 11:00 a.m. Section 2: 11:00 am - noon. Recitation: TBA Office Hours: Will be posted on WebCT Textbook: The required textbook for this course will be: Wonnacott, Thomas H. And Ronald J. Wonnacott, Introductory Statistics for Business and Economics, Fifth Edition, John Wiley & Sons, New York, 2009. Course Requirements: Mandatory attendance at lectures and recitation (attendance will be taken and recorded), the completion of course assignments, two midterms, a data project, and a final exam. Grading in the course will be as follows: 1. Assignments (15% of grade) I will assign 8 assignments over the course of the semester. You are required to turn in all of these exercises. You must do these exercises on your own. Assignments will be due in class (due dates are given in the syllabus). NO late assignments will be accepted. 2. Midterm exams (50%) - There will be 2 midterm exams given during the semester, each worth 25%. 3. Final exam (35%) to be held during the final exam period. Please note that there will be NO make-up exams given. Absence from an exam will be excused only for a serious illness or bereavement (which must be documented). A student who is unable to take the final exam for a legitimate reason MUST obtain advance authorization from the Office of Undergraduate Academic Affairs. There are NO EXCEPTIONS to these rules. Special Accommodations: If you are a student with a documented disability on record at Brandeis University and wish to have a reasonable accommodation made for you in this class, please see me immediately. Please keep in mind that reasonable accommodations are not provided retroactively. Academic Honesty: You are expected to be honest in all of your academic work. Instances of alleged dishonesty will be forwarded to the Office of Campus Life for possible referral to the Student Judicial System. Potential sanctions include failure in the course and suspension from the University. If you have any questions about my expectations, please ask. Academic dishonesty will not be tolerated and will be vigorously prosecuted.
DATES TO REMEMBER Monday, September 5 Thursday, September 29 Wednesday, October 5 Monday, October 10 Tuesday, October 11 Thursday, October 13 Monday, October 17 Thursday, October 20 Thursday, November 10 November 23-25 Monday, December 12 Labor Day. No class. Rosh Hashanah. No class. Midterm #1: in class. Class cancelled. Class cancelled. Sukkot. No class. Brandeis Thursday. Class will be held. Shmini Atzeret: No class. Midterm #2: in class. Thanksgiving Break. No class. Last class. September 8: Assignment #1 September 15 Assignment #2 September 26: Assignment #3 October 17: Assignment #4 October 26: Assignment #5 November 2: Assignment #6 November 9: Assignment #7 December 7: Assignment #8 Note: All assignments will be posted on WebCT. ASSIGNMENT DUE DATES (Tentative) ADDITIONAL REQUIREMENTS You will be required to purchase a NON-PROGRAMMABLE calculator for this class. This will be the ONLY calculator that will be allowed for use in the exams. There will be no exceptions to this rule. This means that you may NOT bring in a programmable graphing calculator (whether or not you can show that there are no stored programs). Your calculator should be able to perform square roots, but nothing more complicated will be necessary. If your calculator does not meet these specifications, you will have to do without a calculator for the exam. You may not use your cell-phone or any other device as a calculator.
TENTATIVE OUTLINE I strongly recommend that you do the day s readings BEFORE lecture. SEPT 1 THURS Introduction: The role of probability and statistics in economic analysis. Overview of the course. Introduction to the notion of population versus sample. Discussion on types of data: nominal, ordinal, interval, ratio. Describing data in a meaningful way through descriptive statistics: frequencies, relative frequencies, percentiles, measures of central tendencies Read: W&W 1.1-1.3 SEPT 5 MON Labor Day. No class. SEPT 7 WEDS Descriptive Statistics. More on frequencies, relative frequencies and percentiles. The relationship between different measures of central tendencies (means, modes, medians). Various measures of dispersion. The effect of scale on measures of the mean and the variance. Read: W&W 2.1 2.3, 2.5-2.6 SEPT 8 THURS Introduction to Probability. What is a sample space? What is an event? Manipulating the event space: intersections and unions of events. Compliments and mutually exclusive sets. Relationship between relative frequencies and probabilities. Read: W&W 3.1-3.3 Exercise 1 due. SEPT 12 MON An Axiomatic Approach to Probability. Discrete versus continuous probability distributions. Read: W&W 3.4-3.5 SEPT 14 WEDS Conditional Probabilities. Examples of conditional probabilities. Introduction to Bayes Theorem. Read: W&W 3.6-3.7 SEPT 15 THURS Conditional Probabilities (continued). More on Bayes Theorem. Examples. Introduction to random variables. Exercise 2 due. SEPT 19 MON Random Variables. What is a random variable? Describing a random variable: means and variances of random variables. A slight detour: combinatorics with and without replacement. Examples. Read: W&W 4.1-4.2
SEPT 21 WEDS A Short Detour: Combinatorics cont. More examples of combinations with and without replacement. SEPT 22 THURS Probability Distributions for Discrete Random Variables. Definition of a discrete probability distribution function. Calculating the mean and variance of a discrete random variable. The expectations operator. Introduction to the Binomial distribution. Examples of the Binomial. Read: W&W 4.3 SEPT 26 MON Probability Distributions for Continuous Random Variables. Functions of a Single Random Variable. Definition of a continuous probability distribution function. Calculating the mean and variance of a continuous random variable. Introduction to the Normal and Standard Normal distribution. The relationship between the Binomial and the Normal distribution functions. Important facts about the Normal distribution. Creating new random variables through functions. Determining the new probability distribution function. Calculating the mean and the variance. The case of a simple linear transformation. Read: W&W 4.4-4.6 Exercise 3 due. SEPT 28 WEDS Functions of a Single and Several Random Variables, cont d. More on the Normal distribution (how to read the table.) Creating new random variables that are functions of several random variables. Constructing the probability distribution function for the new variable. Read: W&W 5.1-5.2 SEPT 29 THURS Rosh Hashanah. No Class OCT 3 MON Review for midterm. OCT 5 WEDS Midterm #1, in class OCT 6 THURS Go over exam. OCT 10 MON Class Cancelled. OCT 11 TUES Class Cancelled. OCT 12 WEDS Joint Densities and Distributions. Probability distribution functions for functions of several random variables. Random samples. Independent random variables. OCT 13 THURS Sukkot. No class. OCT 17 MON Covariance and Correlation. Sampling Properties. Properties of Good Estimators. Variance measures for functions of random variables. Measures of covariance and correlation between random variables. Interpretation of these measures. Discussion
of unbiasedness, efficiency and consistency. How do you determine if an estimator has these properties? Read: W&W 5.2-5.3 Read: W&W 6.1-6.4 Read: W&W 7.1-7.4 Exercise 4 due. OCT 19 WEDS The Central Limit Theorem. Probability distribution for the sample mean. Discussion of sampling issues. OCT 20 THURS Shmini Atzeret. No Class. OCT 24 MON Confidence Intervals. What is a confidence interval and what can it be used for? Constructing confidence intervals (two-sided). Setting the confidence level. Using the Z distribution. Read: W&W 8.1-8.2 OCT 26 WEDS Confidence Intervals, cont d. How to construct a one-sided confidence interval. What to do if the population variance is unknown. Using the Student t-distribution. Exercise 5 due. OCT 27 THURS Comparing Populations. Comparing means of independent samples and paired samples. Read: W&W 8.3-8.4 OCT 31 MON Hypothesis Testing. Designing a statistical test. The null and alternative hypothesis. Constructing a two-sided test using the confidence interval approach. Read: W&W 9.1-9.3, 9.6 NOV 2 WEDS Hypothesis Testing, contd. Constructing a hypothesis test using the test of significance approach. Introduction to one-sided hypothesis testing. Exercise 6 due. NOV 3 THURS One Sided Hypothesis Testing, contd. More on one-sided hypothesis testing. Using p values. NOV 7 MON Type I and Type II Errors. What is the significance of Type I and II errors? Determining which one you might be committing. Calculating Type I and Type II errors. Read: W&W 9.4-9.5 NOV 9 WEDS More on Type I and Type II Errors.
Read: W&W 11.1-11.3 Class Handout Exercise 7 due. NOV 10 THURS Review for Midterm #2. NOV 14 MON Return exam and go over solutions. NOV 16 WEDS Introduction to Regression Analysis. The Bivariate Model. What is econometrics? What can we do with it? The importance of samples versus populations again. Read: Class handout NOV 17 THURS Deriving an estimator for the bivariate model: the Least Squares Model. NOV 21 MON Properties of the Ordinary Least Squares (OLS) Model. The Gauss Markov assumptions. Proof of the Guass-Markov Theorem. NOV 23-25 WEDS Thanksgiving Break. No classes. NOV 28 MON Proof of the Gauss-Markov Theorem, cont d. NOV 30 WEDS Interpreting the Bivariate Model. DEC 1 THURS Hypothesis testing and goodness of fit. DEC 5 MON Dummy variables. DEC 7 WEDS The nitty-gritty: How do you do this in practice, and what does it really mean? Exercise 8 due. DEC 8 THURS Limitations of the bivariate model a hint of what s to come. DEC 12 MON Review for Final Exam.