## STAT-440-640 Advanced Linear Modeling - Regression & Time Series Analysis

Mathematics, Statistics & Computer Science Department

COURSE NO./TITLE: STAT-440/640 Advanced Linear Modeling – Regression & Time Series Analysis

CREDIT: 3

CATALOG DESCRIPTION: Multiple Regression, Inference about Regression Parameters, Remedial Regression Measures, Quantitative and Qualitative Regression, Model Selection/ Validation, Nonlinear Regression, Neural Networks, Logistic and Poisson Regression, Generalized Linear Models, Time Series, Smoothing, Stochastic Time Series, Moving Average and Autoregressive Models, Auto Regressive Integrated Moving Average (ARIMA), Estimating and Forecasting with Time Series.

Prerequisite: STAT-332 Probability & Mathematical Statistics II or permission of instructor.

TEXTBOOK: FORECASTING, TIME SERIES & REGRESSION, 4th Ed., by Bowerman (adopted 8/1/06)

OBJECTIVES: Upon completing the course students will be able to:

1. Regression
• Calculate ordinary least square estimates of the parameters of single and multiple
linear regression models.
• Test hypotheses and construct confidence intervals for the parameters of single
and multiple linear regression models, including tests involving more than one
parameter.
• Determine aptness of a regression model using:
o Analysis of the residuals, and
o F test for lack of fit.
• Perform appropriate data transformations and remedial measures when the data
set is observed to possess one or more of the following characteristics:
o Non-constancy of error variances (heteroscedasticity),
o Non-independence of error terms (serial correlation),
o Multicollinearity,
o Nonlinearity of the regression function.
• Perform analysis of variance in regression models, prepare Analysis of Variance
(ANOVA) tables and test hypotheses using relevant t and F statistics.
• Determine estimates of, and confidence intervals for new observations using
regression (including stepwise and piecewise linear) models.
• Formulate and analyze regression models using dummy variables.
2. Time Series
• Distinguish between Regression and Correlation models, and calculate elasticity
and partial correlations.
• Demonstrate familiarity with intrinsically nonlinear regression models, and in
particular set up least square normal equations to estimate the parameters of such
models using appropriate software.
• Distinguish between ordinary least square and Generalized Linear Models (GLM)
and utilize GLM procedures.
II. Time Series
• Distinguish the basic difference between Regression and Time Series models, and
thereby be able to recognize when a Time Series model should be used.
• Distinguish between deterministic and Stochastic Time Series models.
• Recognize characteristics of Stationary Time Series and compute autocorrelation
functions.
• Analyze data using a Random Walk model.
• Estimate the parameters of an Auto Regressive Integrated Moving Average
(ARIMA) model, and the simpler models Moving Average (MA), Auto
Regressive (AR), and Auto Regressive Moving Average (ARMA) as special
cases.
• Generate forecasts using ARIMA and simpler models, and develop confidence
intervals for the forecasts.
• Demonstrate a familiarity with properties of ARIMA forecasts.
• Run diagnostic checks validating a specified Time Series Model.
Graduate students will be assigned extra self study in the following topics and
encouraged to write their project using topics in these areas.
• Distinguish between Regression and Correlation models, and calculate elasticity
and partial correlations.
• Demonstrate familiarity with intrinsically nonlinear regression models, and in
particular set up least square normal equations to estimate the parameters of such
models using appropriate software.
• Distinguish between ordinary least square and Generalized Linear Models (GLM)
and utilize GLM procedures.
• Distinguish between deterministic and Stochastic Time Series models.
• Demonstrate a familiarity with properties of ARIMA forecasts.

COURSE OUTLINE:

1. Introduction to Forecasting: Methods, Software
2. Review of Single Variable Regression Models and Matrix Algebra
3. Multiple Regression Models
4. Serial Correlation and Heteroscedasticity
5. Regression and ANOVA Tables
6. Inference in Regression
7. Nonlinear Models
8. Generalized Linear Models
9. Time Series Models
10. Smoothing
11. Stochastic Time Series Models
12. MA, AR, ARMA and ARIMA Models
13. Estimating and Forecasting with Time Series Models
14. Properties of ARIMA Forecasts
15. Combined Regression and Time Series Models