Contents Ordinary Least Squares

  1. Overview
  2. Introduction
  3. Linear Regression
    1. Linear Regression in R
      1. Calculate OLS estimator manually in R
      2. Construct the OLS estimator as a function in R
    2. Linear Regression in STATA
    3. Linear Regression in Julia
      1. Multiple Regression in Julia
  4. Theoretical Derivation of the Least Squares Estimator
  5. Gauss Markov Theorem
    1. Proof Gauss Markov Theorem
  6. Gauss Markov (OLS) Assumptions
    1. Linear Parameter and Correct Model Specification
    2. Full Rank of X Matrix
    3. Exogenous Explanatory Variables
    4. Independent and Identically Distributed Error Terms
      1. Consequences when the Expected Value of the Error Term is Non-Zero
      2. Consequences of Heteroscedasticity and how to solve them
        1. Calculate Robust Standard Errors
        2. Calculate Clustered Standard Errors
    5. Normal Distributed Error Terms
  7. Coefficient of Determination or R2
    1. Relationship between Coefficient of Determination & Squared Pearson Correlation Coefficient
  8. Omitted Variable Bias
    1. Overview
    2. Introduction
    3. Understanding the Bias
    4. Explanation and Example
    5. Consequences
    6. What can we do about it?
    7. Concluding Remarks
  9. Robust Standard Errors
    1. Calculate Robust Standard Errors in R
    2. Calculate Robust Standard Errors in STATA
  10. Clustered Standard Errors
    1. Calculate Clustered Standard Errors in R
    2. Calculate Clustered Standard Errors in STATA