UsefulLinks
Statistics
Statistics with R
1. Introduction to R and Statistical Computing
2. R Fundamentals and Basic Operations
3. R Package System
4. R Data Structures
5. Data Import and Export
6. Data Cleaning and Preprocessing
7. Data Manipulation with dplyr
8. Descriptive Statistics
9. Data Visualization Fundamentals
10. Advanced Data Visualization with ggplot2
11. Probability Theory
12. Probability Distributions
13. Sampling and Sampling Distributions
14. Statistical Inference Foundations
15. Hypothesis Testing Framework
16. One-Sample Tests
17. Two-Sample Tests
18. Chi-squared Tests
19. Analysis of Variance (ANOVA)
20. Correlation Analysis
21. Simple Linear Regression
22. Regression Diagnostics
23. Multiple Linear Regression
24. Generalized Linear Models
25. Nonparametric Statistics
26. Introduction to Time Series Analysis
27. Introduction to Machine Learning
28. Reproducible Research
29. Statistical Computing Best Practices
23.
Multiple Linear Regression
23.1.
Multiple Regression Model
23.1.1.
Model with Multiple Predictors
23.1.2.
Matrix Notation
23.1.3.
Assumptions
23.2.
Model Fitting
23.2.1.
lm() with Multiple Predictors
23.2.2.
Categorical Predictors
23.2.3.
Interaction Terms
23.3.
Interpreting Multiple Regression
23.3.1.
Coefficient Interpretation
23.3.2.
Holding Other Variables Constant
23.3.3.
Partial Effects
23.4.
Model Assessment
23.4.1.
Multiple R-squared
23.4.2.
Adjusted R-squared
23.4.3.
F-test for Overall Significance
23.4.4.
Individual Coefficient Tests
23.5.
Multicollinearity
23.5.1.
Definition and Problems
23.5.2.
Detection Methods
23.5.2.1.
Correlation Matrix
23.5.2.2.
Variance Inflation Factor
23.5.2.3.
Tolerance
23.5.3.
Addressing Multicollinearity
23.6.
Variable Selection
23.6.1.
Forward Selection
23.6.2.
Backward Elimination
23.6.3.
Stepwise Selection
23.6.4.
Best Subsets
23.6.5.
Information Criteria
23.6.5.1.
AIC
23.6.5.2.
BIC
23.7.
Model Comparison
23.7.1.
Nested Model Tests
23.7.2.
Cross-validation
23.7.3.
Model Selection Criteria
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22. Regression Diagnostics
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24. Generalized Linear Models