Statistical Learning and Linear Regression Essentials
Posted by Anonymous and classified in Mathematics
Written on in
English with a size of 7.23 KB
Introduction to Statistical Learning
Key Notation
- Y: Response (dependent/output) variable - quantitative or qualitative
- X₁,...,Xₚ: Predictors (features/covariates/independent variables)
- p: Number of predictors
- n: Number of observations
- i: Subject index (i = 1,...,n)
- j: Variable index (j = 1,...,p)
- Data: (Yᵢ, Xᵢ), i = 1,...,n
Types of Learning
- Supervised learning: Have both Y and X (prediction or inference) - PRIMARY FOCUS
- Unsupervised learning: Have X but no Y
Model for Data
Yᵢ = f(Xᵢ) + εᵢ, i = 1,...,n Assumptions: E(εᵢ) = 0, var(εᵢ) = σ², εᵢ are mutually independent Properties: E(Yᵢ|Xᵢ) = f(Xᵢ), var(Yᵢ|Xᵢ) = σ²
Prediction vs Inference
| Prediction | Inference |
|---|---|
| ˆY = ˆf(X) | Understand relationship between Y and X |
| ˆf can be black |