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.