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Introduction to Regression (Population regression funciton # (Dependent…
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
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Dependent variable: Regressand
Explanatory variable: Regressor
Regression parameters:Intercept, Slope Coefficient
Error Distrubance
Simple regression function
Residual
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Regression parameter estimates
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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
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Minimum variance
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Consistent
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Normally distributed
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Testing hypotheses