Material for R

You may find this pdf useful to get started with R.

Review

  • Probability and Statistics

The Simple Regression Model

  • Definition of the Simple Regression Model

  • Deriving the Ordinary Least Squares Estimates

  • Properties of OLS

  • Fitted values and residuals

  • Algebraic properties of OLS statistics

  • Goodness-of-fit

  • Units of Measurement and Functional Form

  • Expected Values and Variances of the OLS estimators

Regression Analysis: Inference

  • Hypothesis testing

  • Sampling Distribution of the OLS estimators

  • Testing hypothesis about a single population parameter

  • Testing against one-sided alternatives

  • Two-sided alternatives

  • Computing p-values for t-tests

  • Confidence intervals

Multiple Regression Analysis

  • Motivation for Multiple Regression

  • Mechanics and Interpretation of OLS

  • Interpreting the OLS regression equation

  • Meaning of “holding other factors fixed’’

  • Changing more than one independent variable simultaneously

  • Partialling out interpretation of multiple regression

  • Comparison of simple and multiple regression estimates

  • Goodness-of-fit

  • Expected values of the OLS estimates

  • Including irrelevant variables in a regression model

  • Omitted variable bias

  • Variance of the OLS estimators

  • Components of the OLS variances, multicollinearity

  • Misspecified models

  • Efficiency of OLS

  • Testing multiple linear restrictions; the F - test

Multiple Regression Analysis with Qualitative Information

  • Binary (or Dummy) Variables

  • A single dummy independent variable

  • Using dummy variables for multiple categories

  • Interactions involving dummy variables