• MBA 8370/8380 Course Companion
  • Preface
    • About this book…
    • Acknowledgements
  • MBA 8370
  • 1 Introduction
    • 1.1 The “Big Picture” of Statistics
    • 1.2 The Vocabulary of Statistics
    • 1.3 Descriptive Measures
      • 1.3.1 Central Tendency
      • 1.3.2 Variation
      • 1.3.3 Measures of shape
      • 1.3.4 Covariance and Correlation
  • 2 Data Collection and Sampling
    • 2.1 Sampling Distributions
    • 2.2 Sampling Bias - two examples
      • 2.2.1 Dewey Defeats Truman?
      • 2.2.2 98.6?
    • 2.3 Sampling Methods
      • 2.3.1 Simple random sampling
      • 2.3.2 Systematic Sampling
      • 2.3.3 Stratified Sampling
      • 2.3.4 Cluster Sampling
    • 2.4 Sampling in Practice
    • 2.5 Sampling and Sampling Distributions
      • 2.5.1 An Application
  • 3 Getting Started with R
    • 3.1 The R Project for Statistical Computing
    • 3.2 Before you Install… Posit (RStudio) Cloud?
    • 3.3 Downloading and installing R
      • 3.3.1 Choosing a Mirror
      • 3.3.2 Download and install the correct version
      • 3.3.3 Downloading and installing RStudio
    • 3.4 Taking Stock
    • 3.5 Coding Basics
      • 3.5.1 Installing Packages
      • 3.5.2 Assigning Objects
      • 3.5.3 Listing, Adding, and Removing
      • 3.5.4 Importing Data
      • 3.5.5 Manipulating Data
      • 3.5.6 Subsetting Data
    • 3.6 Data Visualization
      • 3.6.1 Histograms
      • 3.6.2 Line, bar, and Scatter Plots
      • 3.6.3 Boxplots
      • 3.6.4 Much more out there
  • 4 The Central Limit Theorem
    • 4.1 The CLT (Formally)
    • 4.2 Application 1: A Sampling Distribution with a Known Population
    • 4.3 Application 2: A Sampling Distribution with an Unknown Population
      • 4.3.1 The Sample
    • 4.4 The Punchline
  • 5 Confidence Intervals
    • 5.1 A Refresher on Probability
      • 5.1.1 Application 1
      • 5.1.2 Application 2
    • 5.2 Deriving a Confidence Interval
      • 5.2.1 Application 3
      • 5.2.2 What if we want to change confidence?
      • 5.2.3 What happens to the size of the confidence interval when we increase our confidence?
    • 5.3 What to do when we do not know \(\sigma\)
      • 5.3.1 Student’s t distribution versus Z distribution…
      • 5.3.2 Application 4
    • 5.4 Determining Sample Size
    • 5.5 Concluding Applications
      • 5.5.1 Light Bulbs (Last Time)
      • 5.5.2 Returning to the Philadelphia School Policy Application
  • 6 Hypothesis Tests
    • 6.1 Anatomy of a Hypothesis Test
    • 6.2 Steps to a hypothesis test
    • 6.3 Two methods for conducting a hypothesis test (when \(\sigma\) is known)
      • 6.3.1 Rejection Region Method
      • 6.3.2 P-value Approach
    • 6.4 Two-sided vs One-sided Test
    • 6.5 Conducting a hypothesis test (when \(\sigma\) is unknown)
    • 6.6 Appendix: A note on calculating P-values
      • 6.6.1 The Problem
      • 6.6.2 How to calculate p-values
  • MBA 8380
  • 7 Simple Linear Regression
    • 7.1 A Simple Linear Regression Model
      • 7.1.1 What does a regression model imply?
      • 7.1.2 The REAL Simple Linear Regression Model
    • 7.2 Application: Predicting House Price Based on House Size
    • 7.3 Ordinary Least Squares (OLS)
      • 7.3.1 B.L.U.E.
    • 7.4 Decomposition of Variance
      • 7.4.1 The \(R^2\)
      • 7.4.2 What is a good \(R^2\)?
      • 7.4.3 Standard Error of the Estimate
    • 7.5 Assumptions of the Linear Regression Model
      • 7.5.1 Linearity
      • 7.5.2 Independence of Errors
      • 7.5.3 Equal Variance
      • 7.5.4 Normality of Errors
    • 7.6 A Concluding Application
    • 7.7 Appendix: Statistical Inference
      • 7.7.1 Confidence Intervals (around population parameters)
      • 7.7.2 Hypothesis Tests
      • 7.7.3 Confidence Intervals (around forecasts)
    • 7.8 Up Next…
  • 8 Multiple Linear Regression
    • 8.1 Application: Explaining house price in a multiple regression
      • 8.1.1 The Importance of “Controls”
    • 8.2 Adjusted \(R^2\)
      • 8.2.1 Abusing an \(R^2\)
      • 8.2.2 An Adjusted \(R^2\)
    • 8.3 Statistical Inference
      • 8.3.1 Recalling the Concept of Statistical Inference
      • 8.3.2 Confidence Intervals (around population parameters)
      • 8.3.3 Hypothesis Tests
      • 8.3.4 Confidence Intervals (around forecasts)
    • 8.4 A Concluding Application
      • Interpretation
      • Confidence Intervals
      • Hypothesis Tests
      • Forecasts
  • 9 Collinearity
    • 9.1 An Application
    • 9.2 What does Collinearity do to our regression?
    • 9.3 How to test for Collinearity?
      • Correlation Coefficients
      • Variance Inflation Factors (VIFs)
      • 9.3.1 An Application:
    • 9.4 How do we remove Collinearity?
      • Sometimes removing collinearity might involve multiple rounds
    • 9.5 A Concluding Application
  • 10 Qualitative (Dummy) Variables
    • 10.1 Intercept dummy variable
    • 10.2 Slope dummy variable
    • 10.3 What if there are more than two categories?
    • 10.4 A Concluding Application
    • 10.5 Another Concluding Application
      • Make a Nominal Series a Real Series
      • Remove a Trend
      • Remove Seasonality
  • 11 Functional Forms
    • 11.1 Derivatives
    • 11.2 Why consider non-linear relationships?
    • 11.3 The Log transformation
      • The derivative of the log function
      • Log-log and Semi-log models
      • Application
    • 11.4 The Quadratic transformation
      • Application
    • 11.5 The Reciprocal transformation
      • Application
    • 11.6 Conclusion
    • 11.7 A Concluding Application
      • A Residual Analysis
      • Log Transformation
      • Quadratic Transformation
      • Reciprocal Transformation
  • 12 Joint Hypothesis Tests
    • 12.1 Simple versus Joint Hypothesis Tests
      • Application
    • 12.2 Conducting a Joint Hypothesis Test
      • 1. Estimate an Unrestricted Model
      • 2. Estimate a Restricted Model
      • 3. Construct a test statistic under the null
      • 4. Determine a P-value and Conclude
    • 12.3 Applications
      • Application 1: A wage application
      • Application 2: Constant Returns to Scale
    • 12.4 A Concluding Application
  • Published with bookdown

Course Companion for MBA 8370 and MBA 8380

Course Companion for MBA 8370 and MBA 8380

Scott Dressler

2024-08-22