DISC 3322
STATISTICAL ANALYSIS FOR BUSINESS APPLICATIONS II

Prof. Julio León Peixoto

OBJECTIVE AND TENTATIVE COURSE OUTLINE

OBJECTIVES

The typical business executive has access to large quantities of data obtained from a variety of sources. These data may contain information that is useful to make decisions. However, the size and complexity of many data bases make the extraction of practical information difficult without the use of statistical methods. Statistics is an area of science concerned with

• the generation of high quality data (through designs of experiments and sampling procedures),
• the analysis of data (i.e., how to summarize data and "make sense" out of it), and
• the use of data for decision making (such as making predictions about a large population using data obtained from a relatively small sample).

This course gives an introduction to the main statistical techniques of data analysis. The emphasis is in the description of the techniques rather than in the presentation of the underlying mathematical theory. The course has two main objectives:

1. to inform all students of the general principles of statistical methodology ("statistical literacy objective") and
2. to prepare some students for subsequent courses in Statistics ("prerequisite objective").

TENTATIVE COURSE OUTLINE

• INTRODUCTION: Definitions of statistics, parameter, statistic, population, sample, flows of information between population and sample, definition of descriptive statistics, definition of probability theory, definition of statistical inference, summation notation.
• ESTIMATION AND TESTS OF HYPOTHESES: Student's t distribution, confidence intervals, tests of hypotheses, inferences on a population mean, sampling distribution of the difference between two independent statistics, inferences on the difference between two population means under independent sampling (equal and unequal variances), paired comparison experiments, testing the equality of two population variances, inferences on a population proportion, inferences on the difference between two population proportions, determining the sample size.
• ONE-WAY ANALYSIS OF VARIANCE (COMPARISON OF SEVERAL MEANS): Definition of analysis-of-variance models, types of analysis-of-variance models, balanced and unbalanced designs, elementary principles of design of experiments, completely randomized design, among- and within-treatments sums of squares, inferences on treatment contrasts, main and interaction effects.
• SIMPLE LINEAR REGRESSION: Assumptions, the least-squares principle, sums of squares, analysis-of-variance table, inferences on the intercept and slope, inferences on the error variance, coefficients of correlation and determination, assessing the usefulness of the model, F distribution, prediction, prediction bands, dangers in extrapolating outside the observed range.
• MULTIPLE REGRESSION: Assumptions, nonlinear effects, transforming nonlinear models into linear models, dummy variables, interaction effects, least-squares estimation, analysis-of-variance table, inferences on regression coefficients, overall and partial F tests, prediction, unadjusted and adjusted coefficients of determination, shortcomings of R² as a measure of goodness of fit, critical value of R², relationships between R² and F, multicollinearity, residual analysis, regression diagnostics, detection of outliers and other unusual observations, introduction to model building, stepwise and related variable selection methods.
• CATEGORICAL DATA (COUNT DATA) ANALYSIS: Inferences about proportions, comparing two proportions, comparing populations from two-way tables, tests of independence with two-way tables.
• TIME SERIES: Introduction to time series analysis, autoregressive models, moving average models, ARIMA models.