STAT525 REGRESSION THEORY AND METHODS
| Course Code: | 2460525 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Statistics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. BARIŞ SÜRÜCÜ |
| Offered Semester: | Fall Semesters. |
Course Objectives
By the end of this course, students will be able to:
Formulate and fit simple and multiple linear regression models using least squares (LS) and generalized least squares (GLS). State and apply the Gauss–Markov theorem, interpreting its assumptions and implications for BLUE estimators.Diagnose model adequacy via residual analysis, influence diagnostics (e.g., leverage, Cook’s distance), and checks for nonlinearity, heteroscedasticity, and non?normality. Remedy model deficiencies using transformations (e.g., Box–Cox, log) and appropriate weighting schemes. Detect and address multicollinearity using VIF and related tools; justify remedies (centering, variable selection, or regularization). Design and execute variable selection (best subset, stepwise/forward/backward) with principled criteria (AIC, BIC) and validate choices via cross?validation.Build and interpret GLMs for binary and count data (logistic, Poisson/negative binomial), including link functions, dispersion checks, goodness?of?fit, and practical metrics (ROC/AUC, calibration, deviance). Robust Regression methods. Non-Parametric Regression, Regression with Non-normally Distributed Errors, Regression with Stochastic Predictors. Implement algorithms in statistical software (e.g., R or Python). Carry out a computer aided project: pose a substantive question, assemble and clean data, justify modeling choices, assess robustness, and present actionable conclusions with ethical and reproducible practices.
Course Content
General regression models, residual analysis, selection of regression models, response surface methods, nonlinear regression models, experimental design and analysis of covariance models. Least squares, Gauss-Markov theorem. Confidence, prediction and tolerance intervals. Simultaneous inference, multiple comparison procedures.
Course Learning Outcomes
- Formulate and apply statistical regression theory
- Formulate and apply advanced methods in statistical regression modeling
- Design and implement advanced methods in regression analysis for applications
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Ability for converting theoretical, methodological, and computational statistical knowledge into analytical solutions in researches requiring statistical analyses. | ✔ | |||
| 2 | Ability for specifiying problems in real life situations bearing uncertainty, forming hypotheses, modeling, application, and interpreting the results. | ✔ | |||
| 3 | Ability for using current technology, computer softwares for statistical applications, computer programming for specific problems when necessary, writing computer codes for speeding up statistical calculations, organizing and cleaning databases, and preparing them for statistical analyses, and data mining. | ✔ | |||
| 4 | Ability for taking part in intra/inter disciplinary team work, efficient use of time, taking responsibility as a team leader, and entrepreneurship. | ✔ | |||
| 5 | Ability for taking responsibility in solitary work and producing creative solutions. | ✔ | |||
| 6 | Ability for keeping up-to-date with current advancements in statistical sciences, doing research, being open-minded, and adopting critical thinking. | ✔ | |||
| 7 | Ability for effective communication both in Turkish and English in specification of statistical problems, analyes, and interpretation of findings. | ✔ | |||
| 8 | Ability for using the knowledge in the field of expertise for the welfare of the society. | ✔ | |||
| 9 | Ability for suggesting the researchers in a comprehensible way the appropriate statistical methods for problems in fields that use statistics such as economics, finance, industrial engineering, genetics, and medicine and apply if needed. | ✔ | |||
| 10 | Ability for catalyzing discussions and presentations, public speaking, making presentations, communicating topics of expertise to the audiance in a comprehensible way. | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution