Learning Objectives
5 objectives- Understand the fundamental concepts of linear models and their role in data analysis.
- Perform and interpret simple and multiple linear regression analyses.
- Evaluate the assumptions and goodness of fit of linear regression models.
- Apply techniques for variable selection and address collinearity issues in model building.
- Explore polynomial regression and practical applications of linear models across various fields.
Content Outline
PreviewUnit 3093: Linear Models and Regression Analysis
1. Introduction to Linear Models
- Definition of linear relationships
- Independent vs. dependent variables
- Purpose and applications of linear models in data analysis
2. Simple Linear Regression
- Concept and formulation of simple linear regression
- Fitting a linear equation: y = β0 + β1x + ε
- Interpretation of regression coefficients
- Prediction using simple linear regression
3. Multiple Linear Regression
- Extension from simple to multiple independent variables
- Model formulation: y = β0 + β1x1 + β2x2 + ... + βnxn + ε
- Interpretation of coefficients in multiple regression
- Use cases and examples
4. Assumptions of Linear Regression
- Linearity: relationship between predictors and response
- Independence of errors
- Homoscedasticity: constant variance of errors
- Normality of residuals
- Methods to test assumptions (scatterplots, Durbin-Watson test, residual plots, Q-Q plots)
5. Assessing Model Fit
- Coefficient of determination (R-squared)
- Adjusted R-squared for multiple predictors
- Statistical significance of regression coefficients (t-tests)
- F-test for overall model significance
6. Residual Analysis
- Definition and calculation of residuals
- Interpreting residual plots
- Detecting outliers and influential points
- Validity checks for regression model
7. Variable Selection and Model Building
- Importance of selecting relevant variables
- Stepwise regression (forward selection and backward elimination)
- Criteria for variable inclusion/exclusion (p-values, AIC, BIC)
- Building robust and parsimonious models
8. Collinearity in Linear Models
- Definition and causes of collinearity
- Effects on coefficient estimates and model stability
- Detecting collinearity (Variance Inflation Factor - VIF, condition indices)
- Remedies: variable removal, combining variables, principal component regression
9. Polynomial Regression
- Extending linear models to capture nonlinear relationships
- Model formulation with polynomial terms (e.g., quadratic, cubic)
- Interpretation and visualization of polynomial regression
- Overfitting and model complexity considerations
10. Practical Applications of Linear Models
- Economics: forecasting and trend analysis
- Social sciences: studying relationships between social variables
- Healthcare: predicting patient outcomes
- Engineering: quality control and process optimization
- Case studies demonstrating prediction and decision-making using linear models
Unlock the full outline
Get the complete content outline, learning outcomes and assessment methods for Linear Models.
KSh 20 one-off, or included with a plan
Learning Outcomes
Unlock the outline above to see learning outcomes.
Assessment Methods
Unlock the outline above to see assessment methods.