Introduction to Regression

Background

Focus: Causal effects(ceteris paribus effects)

Gold standard: Randomised Experiments

Probability model of a causal linear relationship

Project: mimic randomised experiment with regression applied to observational data

Conditional mean model

Model assumptions

Population regression funciton #

Dependent variable: Regressand

Explanatory variable: Regressor

Regression parameters:Intercept, Slope Coefficient

Error Distrubance

Simple regression function

Residual #

Regression parameter estimates #

Linear Regression model estimation

Method of moments, Max likelihood

Ordinary Least Squares

Model fit (evaluation)

Sum of squares decomposition

R^2

SER

Statistical properties of coefficient Estimators

Unbiased #

Minimum variance #

Consistent #

Normally distributed #

Testing hypotheses