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PS9591: Regressions and Causal Inference

9 Lecture 4: The Simple Regression Model I

Slides

  • 5 The Simple Regression Model (link)

9.1 Introduction

In the previous lecture, we explored how we can understand causal inference and the importance of random assignment. Experiments allow us to randomize the treatment and create believable counterfactuals. But we cannot solely rely on experiments to estimate causal relations. Thus, we study regression… The lecture slide are displayed in full below:

Figure 9.1: Slides for 4 The Simple Regression Model I.

9.2 Lecture Assignment

  1. Given the population regression function: \(y = 2 + 4x + \mu\), use simulated data to show that OLS yields unbiased estimates from a random sample of the population.

  2. Show how the mean and standard deviation of the distribution of the \(\beta\)’s from your simulation change with sample size. Plot your results and also create a table.

  3. Show how the mean and standard deviation of the distribution of the \(\beta\)’s from your simulation change with the variance in \(x\). Plot your results and also create a table.

  4. Show how the mean and standard deviation of the distribution of the \(\beta\)’s from your simulation change with the variance in \(y\). Plot your results and also create a table.