The course explores essential statistical modeling techniques for data science and machine learning. Topics include regression, multicollinearity, categorical variables, variable selection, regularization, and logistic regression. Emphasis is placed on interpretation, visualization, and model refinement, addressing nonlinearity and limitations.
Athena Title
Stat Modeling in Data Sci
Non-Traditional Format
This course will be taught 95% or more online.
Prerequisite
STAT 6381E and STAT 6382E
Corequisite
STAT 6385E
Semester Course Offered
Offered summer semester every year.
Grading System
A - F (Traditional)
Student learning Outcomes
Students will construct and interpret statistical models to make objective predictions and quantify variable effects in data science.
Students will build, refine, and assess regression models, addressing issues like multicollinearity, variable selection, and model accuracy.
Students will apply regularization techniques (e.g., Lasso, Ridge) to handle high-dimensional data and improve model performance.
Students will develop and interpret nonlinear models, including polynomial regression and transformations for complex relationships.
Students will construct logistic regression models for binary and multiclass classification problems and evaluate their performance.
Students will visualize and communicate model outputs effectively, using appropriate statistical graphics and performance metrics.
Students will compare statistical modeling approaches, including regression and ANOVA, while recognizing their assumptions and limitations.
Topical Outline
Introduction to Statistical Modeling
• Role of statistical models in data science and machine learning
• Overview of predictive modeling and effect quantification
• Introduction to regression as a fundamental statistical tool
Linear Regression
• Concept and mathematical formulation of linear regression
• Assumptions of linear regression models
• Estimation of coefficients using ordinary least squares (OLS)
Model Interpretation and Visualization
• Interpreting regression coefficients and statistical significance
• Visualizing model results using diagnostic plots
• Communicating model findings effectively
Multivariable Regression Analysis
• Incorporating multiple predictors in regression models
• Identifying and addressing multicollinearity
• Variable selection techniques: stepwise selection, AIC/BIC, and others
• Introduction to regularization methods (Lasso, Ridge, Elastic Net)
Nonlinear Relationships
• Identifying nonlinearity in data
• Variable transformations (e.g., logarithmic, square root)
• Polynomial regression models for capturing nonlinearity
Logistic Regression
• Understanding logistic regression for categorical response variables
• Model fitting and interpretation of odds ratios
• Applications in binary and multiclass classification
• Model evaluation: ROC curves and AUC
Model Diagnostics and Refinement
• Assessing model fit and performance metrics (e.g., R-squared, RMSE, confusion matrix)
• Identifying and addressing influential observations and outliers
• Evaluating assumptions and limitations of regression models
Advanced Topics in Regression Modeling
• Error metrics and their role in model improvement
• Comparing models and choosing the best-fit model
• Generalization and overfitting
Connections to ANOVA
• Relationship between regression and ANOVA models
• Application of ANOVA to compare group means
Applications and Case Studies
• Real-world examples of regression modeling in data science
• Hands-on exercises and projects using R programming
Institutional Competencies Learning Outcomes
Analytical Thinking
The ability to reason, interpret, analyze, and solve problems from a wide array of authentic contexts.
Critical Thinking
The ability to pursue and comprehensively evaluate information before accepting or establishing a conclusion, decision, or action.
