Statistics
Please note: Before scheduling classes, check with the department to determine the availability of courses for the upcoming semester or visit the Statistics website.
A key challenge facing managers is the interpretation of the vast amount of data generated in the world of business today. Modern computing systems now produce large volumes of information whereas previously one could often only rely upon intuition and guesses. Yet this information does not directly answer important business questions. What combination of features is most desirable for consumers? What will sales be next month? How did we do last month? Data analysis and statistics offer a systematic approach that can help provide answers to these questions.
Courses offered by the Statistics Department develop the skills and insights required to make effective use of statistical methods. The courses provide the knowledge needed to select and apply techniques and to communicate statistical results. Interpretation in realistic applications offers guiding examples, and theory is used to motivate and compare alternative schemes. The courses range from a rigorous training in the fundamentals of statistical theory (STAT 430-431) to applications of popular methodologies, such as regression analysis (STAT 701) and forecasting (STAT 711).
Regardless of topic, all of these courses provide useful skills that augment the substantive managerial abilities of students. Courses also provide exposure to computer software that implements key techniques.
Program RequirementsThe Statistics major may be tailored in accordance with student’s interests, which may involve a second major. Five credit units are required and STAT 621 may contribute 0.5 credit units. Some courses offered by other departments are permitted (students who wish to include courses from other departments in the major should request permission to include these from the Statistics Department advisor and file this permission with the MBA Program Office). Courses taken on a Pass/Fail basis cannot be counted toward the major.
The following courses offered by the Department of Statistics are eligible for the major:
STAT 430
Probability
Description: Discrete and continuous sample spaces and probability; random variables, distributions, various popular models.
Format: Lecture and discussion. Homework problems. Two midterms and a final exam.
Prerequisites: Students should be comfortable with basic integral calculus.
STAT 433
Stochastic Processes
Description: This course is to be a basic introduction to stochastic processes. The primary focus will be on Markov chains both in discrete time and in continuous time. By focusing attention on Markov chain, we can discuss many interesting models (from physics to economics). Topics covered include: stable distributions, birth-death processes, Poisson processes, time reversibility, random walks, Brownian motion and Black-Scholes.
Format: Lecture and discussion. Homework problems. Two midterms and a final exam.
STAT 510
Probability and Statistics for Business and Economics
Description: This course provides an introduction to the basic tools needed to develop probability models that describe data. The material of the course is best summarized with an example. Suppose that we have just completed a marketing survey of 50 potential customers. As part of the survey, these customers were asked if they would purchase a new product at a specific price. Based on the results of this survey, the product manager must arrive at a price for the product when national marketing begins, and must also provide an estimate of ultimate sales. This course develops models that provide a systematic approach to this task and many other problems. The course seeks to provide students with sufficient background so that they can develop and apply probability models in varying domains. This background includes understanding the essential ideas of probability and randomness and the manipulation of and relationships among various popular models.
Format: Lecture and discussion. Assigned and graded exercises, midterm, and final exam.
Prerequisites: Students should be comfortable with basic integral calculus.
STAT 511
Statistics for Business and Economics
Description: This course introduces statistical models used to describe the relationships among multiple variables. Relevant business applications include modeling how various factors affect sales, the interaction of price and quality, maximization of portfolio stability, and characterizing the factors that affect brand choice. The presentation operates at a level that opens the “black box” and reveals underlying conceptual foundations. This exposure permits students to go beyond the straightforward application of techniques and develop critical judgment. The key statistical methods developed in this course include multiple regression analysis with graphical diagnostics, econometric models, analysis of variance, maximum likelihood estimation and testing, robust and nonparametric methods for comparison and regression, and logistic regression and other models for qualitative choice problems. The theoretical basis for each model is formulated and then applied to an actual set of data using computer software.
Requirements: Assigned and graded exercises, midterm, and final exam.
Prerequisite: STAT 510 or permission of instructor.
STAT 621 (.5 cu)
Statistical Analysis for Management
Description: See description in Core section.
STAT 622x (.5 cu)
Statistical Modeling
Description: This six-week, elective MBA course continues the required MBA statistics course, Stat 621. It expands the material covered in Stat 621 in several ways, adding both breadth (e.g., logistic regression) and depth to the coverage of regression (e.g., more diagnostics, model selection). The course emphasizes the models for decision making from large data sets, as common in data-mining. Lectures feature extensive analysis of large data sets from marketing, personal finance, and management. The course presumes that students are familiar with the inferential methods covered in Stat 603/621 (including hypothesis tests, confidence intervals, p-values) as well as the use and interpretation of least squares regression models. The course also uses JMP as in Stat 621. Beginning with a review of these concepts, Stat 622 covers related methodologies that produce fits that resemble and extend regression models. The methodologies include those that expand the nature of the predictors (as in the use of special transformations in time series and the construction of regression trees) and allow the use of categorical responses (logistic regression). The course concludes by exploring the relationship between a regression fit to observational data and an analysis of variance estimated from experimental data, as in a conjoint analysis.
Format: Lecture and discussion. Assigned and graded individual and group exercises, data analysis project, and a final exam.
Prerequisite: STAT 621
STAT 701
Advanced Statistics for Management
Description:
This is a course in regression and time series analysis. The regression module is designed to extend understanding of simple linear regression to multiple regression and its applications. One such application is to the problem of forecasting from time-dependent observations or time series. The time series module is designed to acquaint you with issues in methods of forecasting in the real world. Examples arise from finance, marketing, and other functional areas of business research.
Format: Lecture and discussion. Assigned and graded exercises.
Prerequisite: STAT 621 or equivalent.
STAT 711
Forecasting Methods for Management
Description: This course provides an introduction to the wide range of techniques available for statistical forecasting. These range from subjective approaches to highly mathematical procedures. Qualitative techniques, smoothing and decomposition of time series, regression, adaptive methods, autoregressive-moving average modeling, and ARCH formulations will be surveyed. The emphasis will be on applications, rather than technical foundations and derivations. The techniques will be studied critically, with examination of their usefulness and limitations.
Requirements: Assigned and graded exercises.
Prerequisite: STAT 621 or equivalent.
STAT 712
Decision Making Under Uncertainty
Description: Fundamentals of modern decision analysis with emphasis on managerial decision making under uncertainty and risk. The basic topics of decision analysis are examined. These include payoffs and losses, utility and subjective probability, the value of information, Bayesian analysis, inference and decision making. Examples are presented to illustrate the ideas and methods. Some of these involve: choices among investment alternatives; marketing a new product; health care decisions; and costs, benefits, and sample size in surveys.
Format: Lecture and discussion. Homework assignments, a project, and midterm and final exams.
Prerequisite: STAT 511 or STAT 621 or equivalent.
STAT 910
Forecasting and Time Series Analysis
Description: Many types of measurements naturally occur over time. Most macroeconomic data, such as gross national product, stock market returns, or short-term interest rates, are collected sequentially. This sequential behavior characterizes time series data and leads to a collection of models that can accommodate repeated measurements. This course develops a range of models appropriate for the description and prediction of time series data. A by-product of this exposure is a greater appreciation of the assumptions implicit in regression analysis and econometrics. The primary focus is upon developing, applying, and critically evaluating statistical models that are appropriate in varying conditions. A unifying theme in the course is the selection of an appropriate model, and several schemes are offered, ranging from informal graphical methods to sophisticated likelihood methods such as the AIC. The presentation also contrasts the prediction characteristics of the various models. The range of models considered includes the Box-Jenkins ARIMA class, combinations of time series models and regression methods, frequency-domain techniques, models of co-integration and causation, and nonlinear models based on smoothing techniques.
Format: Primarily lecture and discussion with occasional computing recitations. Assigned and graded exercises, data analysis project, midterm, and final exam.
Prerequisite: STAT 511 or STAT 701 or permission of instructor.
STAT 920
Sample Survey Methods
Description: This course will cover the design and analysis of sample surveys. The focus of attention will be on the latter, specifically, classical analyses of random sampling, stratified sampling, cluster sampling, large sample results, and other topics as time permits and students’ interests dictate.
Format: Lecture and discussion.Homework assignments, a final project, and presentation.
Prerequisites: STAT 511 or equivalent with permission of instructor.
STAT 925
Multivariate Analysis: Methods
Description: The multivariate normal distribution and its properties; marginal and conditional distributions; multiple and partial correlation. Samples from the multivariate normal; estimation of parameters, partial correlation, multiple correlation, and regression coefficients; tests of hypotheses. Hypothesis tests and confidence statements for the multinormal mean vector based on the Hotelling T-squared statistic. One-, two-, and repeated-sample cases. Power and sample size determination. Profile analysis. Multivariate analysis of variance and the multivariate general linear model. Applications to standard experimental designs. Linear discrimination and classification for two and several groups; hypothesis tests on covariance matrices. Canonical correlation; principal components and factor analysis. Examples from the social, behavioral, life, and economic sciences.
Format: Lecture and discussion. Midterm and final exams; analysis of a set of multivariate data of the student’s choice (not multiple regression or correlation).
Prerequisites: STAT 511; some facility in computing via statistical packages; a working knowledge of matrix algebra; breadth of intellectual and scientific curiosity beyond immediate applications.