／var／logmarcus chiu

Regression Models／Analysis (Regressor／Predictor／Independent／Input／Feature-Function - Response／Dependent／Output／Outcome) Variable

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  • Regression Analysis - describes the relationship between a set of independent variables {𝑋1, …, 𝑋𝑘} and a dependent variable 𝑌
  • Regression Model of 𝑌 on {𝑋1, …, 𝑋𝑘} is the conditional-expectation/function that measures the relation between 𝑌 and {𝑋1, …, 𝑋𝑘}:
    • ℎ(𝑥1, …, 𝑥𝑘) = 𝑓(𝑥1, …, 𝑥𝑘) = 𝐄{𝑌|𝑋1=𝑥1, …, 𝑋𝑘=𝑥𝑘} = 𝑦̂
  • where:
    • 𝑌 (response/dependent/output/outcome variable) is a variable of interest that we predict based on one or several predictors
    • {𝑋1, …, 𝑋𝑘} (regressor/predictor/independent/input/feature function variables) are a mixture of continuous and/or discrete variables used to predict 𝑌

Regression Model - Types

Parametric Regression (PR) Models

ℎ(𝑥1, …, 𝑥𝑘) = 𝑓(𝑥1, …, 𝑥𝑘) = 𝐄{𝑌|𝑋1=𝑥1, …, 𝑋𝑘=𝑥𝑘} = 𝑦̂ is a parametric function based on coefficient parameters

Non-Parametric Regression (NPR) Models

ℎ(𝑥1, …, 𝑥𝑘) = 𝑓(𝑥1, …, 𝑥𝑘) = 𝐄{𝑌|𝑋1=𝑥1, …, 𝑋𝑘=𝑥𝑘} = 𝑦̂ is a non-parametric function based on data