Download Behavioral Objectives for BUSA 5325: Advanced Statistical Methods

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