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Behavioral Objectives for BUSA 5325: Advanced Statistical Methods The student should be able… I. Before BUSA 5325 A. Statistics, Data and Statistical Thinking 1. To explain the difference between descriptive and inferential statistics 2. To explain how populations and samples differ 3. To define statistical thinking, census, data, qualitative data, quantitative data, survey, variability B. Methods for Describing Sets of Data 1. To define histogram, mean, median, mode, range, skewness, standard deviation, variance, z-score 2. To discuss conditions under which the mean is preferred to the median as a measure of central tendency. 3. To describe the shape, center, and dispersion of a data set verbally, graphically, and/or numerically including construction and use a histogram, box plot, and a cumulative relative frequency line chart (i.e., ogive) C. Probability 1. To define experiment, sample point, sample space, events, union, intersection, complementary events, mutually exclusive events, independent events 2. To explain conditional probability 3. To apply the additive and multiplicative laws of probability 4. To draw a simple random sample D. Discrete Random Variables 1. To identify both discrete and continuous random variables 2. To compute the mean and variance of a discrete random variable defined on a finite sample space 3. To identify binomial random variables and characterize their properties E. Continuous Random Variables 1. To identify normal random variables and characterize their properties 2. To compute probabilities for normal random variables using tables 3. To approximate a binomial distribution with a normal distribution F. Sampling Distributions 1. To explain the concept of a sampling distribution 2. To define error of estimation, point estimator, standard error of the mean, unbiased estimate 3. To state the Central Limit Theorem and discuss how it relates to the sampling distribution of the sample mean G. Inference Based on a Single Sample: Estimation with Confidence Intervals 1. To define bound on the error of estimation, confidence interval, t-statistic 2. To explain how a confidence interval for the sample mean relates to the Central Limit Theorem and the normal distribution 3. To interpret a confidence interval for a parameter 4. To construct a large sample confidence interval for a mean or proportion 5. To construct a small sample confidence interval for a mean 6. To determine sample size for estimating a mean or proportion with a given level of confidence and bound on error of estimation H. Inference Based on a Single Sample: Tests of Hypothesis 1. To define alternative hypothesis, level of significance, null hypothesis, observed significance level (p-value), power of the test, rejection region, test statistic, Type I and Type II error 2. To explain the rationale of hypothesis testing 3. To test hypotheses about means and proportions using the Elements of Hypothesis Testing with both large and small samples 4. To test hypotheses using computed p-values rather than rejection regions 5. To interpret the conclusions from a hypothesis test I. Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses 1. To define paired samples, pooled sample variance 2. To construct a confidence interval for (or test for) differences between means or proportions with data from two large independent samples 3. To construct a confidence interval for (or test for) differences between means with two small independent samples 4. To test for differences between means with paired sample data 5. To test for differences between variances with data from two independent sample 6. To use the z, t, Chi-squared and F tables in the back of the book These objectives correspond to the chapters of the BUSA 5325 text, Statistics for Business and Economics by McClave, Benson and Sincich. Students should have covered topics A through H above in their first course in statistics. Topic I (Chapter 9) provides a good review of the earlier material but may be new for some students. Before beginning BUSA5325, all students should review Chapters 1-8 and work a representative sample of supplementary exercises. II. After BUSA 5325 A. Simple Linear Regression 1. To plot bivariate data as a scattergram using Excel and NCSS 2. To write a bivariate model and estimate the unknown parameters of the model from a data set in Excel and NCSS 3. To interpret the least squares estimates of the slope and intercept (if appropriate) 4. To state the LINE regression assumptions within the context of a specific problem 5. To estimate the standard deviation of the probability distribution of the random error term 6. To statistically evaluate the usefulness of the model 7. To obtain a confidence interval estimate for the slope and interpret 8. To compute and interpret Pearson's correlation coefficient 9. To compute and interpret in context a confidence interval for the mean value of the dependent variable Y given a value of the independent variable X 10. To compute and interpret in context a prediction interval for an individual value of the dependent variable Y given a value of the dependent variable X 11. To analyze residuals for impact on the estimated model coefficients and resulting predictions B. Multiple Regression 1. To write a multivariate model and estimate the unknown parameters of the model from a data set in NCSS 2. To interpret the least squares estimates of the regression coefficients (if appropriate) 3. To state the LINE regression assumptions within the context of a specific problem 4. To obtain an estimate of the variance (sigma squared) 5. To test for the contribution of an individual variable over and above the other variables 6. To obtain confidence intervals for each of the true regression coefficients and interpret them (if appropriate) 7. To test for usefulness of the given model 8. To interpret R-squared, the coefficient of determination, in the context of the problem 9. To model, test and interpret interactions between two variables 10. To obtain prediction intervals for individuals and confidence intervals for the means in NCSS for the dependent variable given a vector of values for the independent variables 11. To interpret the above intervals in context of a problem 12. To analyze residuals and partial residuals to check LINE assumptions 13. To explain the pitfalls of multicollinearity and extrapolation C. Model Building 1. To construct first and second order models with a single quantitative variable using Excel and NCSS 2. To model a qualitative independent variable using dummy variables in NCSS 3. To determine the form of the regression model for each level of the qualitative variable 4. To construct first and second order models with one or more quantitative and qualitative variables 5. To interpret in the context of a particular problem the meaning of a quadratic or interaction term in a model 6. To test portions of a model using the full versus reduced model F-drop test 7. To use NCSS to calculate the parts to the full versus reduced model test 8. To explain what a variable selection technique does in general 9. To calculate all possible regressions using NCSS 10. To identify problems in regression analysis: heteroscedasticity, collinearity, correlated errors, and nonnormality using NCSS 11. To describe the problems associated with collinear independent variables 12. To explain clearly the difference between collinearity and interaction 13. To describe the problems associated with outliers and influential observations 14. To use the hat diagonal values to identify outliers in the X values 15. To state when it is appropriate to remove outliers/influential points 16. To use a residual plot to check assumptions 17. To use a partial residual plot to check for linearity 18. To know how and when to transform the independent and/or dependent variables 19. To compare several different multiple regression models and select the preferred model considering the coefficient of determination, significance of the individual variables, principle of parsimony, LINE assumptions, outliers, high leverage points, and multicollinearity D. Time Series Analysis and Forecasting 1. To construct simple and composite index numbers 2. To describe the CPI-U and the CPI-W 3. To smooth time series data using a moving average or exponential smoothing using Excel and NCSS 4. To plot an overlay of raw time series data, smoothed data, and modeled trend using Excel 5. To identify and describe the four components of time series variation 6. To identify when to use the multiplicative decomposition model and when to use an additive seasonal model 7. To explain the problems occurring when ordinary least squares is used with positively correlated errors. 8. To state the form and use of an autoregressive model 9. To identify a stationary time series using sample autocorrelation coefficients 10. To identify the order of a stationary autoregressive series using partial autocorrelation coefficients 11. To use NCSS to calculate estimated parameters of a decomposition and first order autoregressive forecasting model 12. To compare forecasting models using the MAD criterion for future forecasts 13. To articulate the uncertainties of forecasting even with a model that fits historic data E. Design of Experiments and Analysis of Variance 1. To distinguish between experimental and observational studies 2. To explain principles of experimental design such as randomization, control, blocking, repeat tests, replications 3. To design completely randomized and randomized block experiments 4. To describe the purpose of factorial and fractional-factorial designs 5. To model experimental data using dummy variables in a regression equation 6. To test for main effects and/or interactions 7. To state which means to compare depending on the significance of interaction 8. To use experiment wide error controls 9. To state the assumptions necessary for statistical inferences in the context of an application 10. To use NCSS to perform Analysis of Variance and multiple comparison procedures F. Analysis of Contingency Tables 1. To compute expected frequencies and cell Chi squares with and without NCSS 2. To test the observed association between two qualitative variables for significance 3. To measure the strength of the association between two qualitative variables taking into consideration the level of data for each variable 4. To describe how two qualitative variables are associated G. Overall 1. To compare ‘econometric’ regression models with time series models for forecasting future values of an independent variable using real business or economic data 2. To identify data sets that can be analyzed as a random sample, distinguishing between sub-sets of finite populations and sets of observations of random variables 3. To select an appropriate statistical method for analyzing a business or economic data set with respect to a given question 4. To distinguish between statistical significance and practical importance 5. To frame relevant and important business questions and address them with inferential statistical procedures