Statistics for Economists

The following sections are included:

• Preface
• About the Author
• Acknowledgements
• Contents

The following sections are included:

• Introduction
• Goals
  • Think more clearly
  • Understand uncertainty
  • Understand the world
  • Make decisions under uncertainty
• Who Should I Marry?
• Is Statistics Hard?
• Are Americans in Love?
• Population
• Sample
• Goals
• Exercises

The following sections are included:

• Introduction
• Descriptive Statistics
• Inferential Statistics
• Variables
• Describing Variables
• Graphing Data
  • Pie charts and bar graphs
  • Stem plots
  • Histograms
  • Time series plots
• Numerical Summaries
  • Center of a distribution
  • Spread of a distribution
• Linear Transformations
• Relationships
• Quantitative Data
  • Scatterplot of X and Y
  • Covariance
  • Correlation coefficient
  • Correlation ≠ causality
• Qualitative Data
  • Simpson’s paradox
• Exercises

The following sections are included:

• Introduction
• Classical Probability
• Frequentist Probability
• Subjective Probability
• Back to Classical Probability
  • Ordering n distinct items
  • Permutations of x out of n distinct items
  • Combinations of x out of n distinct items
• Rules of Probability
  • Conditional probability
• The Addition Rule
  • Example
• The Multiplication Rule
  • Examples
• The Subtraction Rule
• Some Examples
  • Some birthdays vs particular birthdays
  • Julius Caesar and you
• Bayes Theorem
  • Lizzie Borden
  • HIV/AIDS?
  • Subjective probability of having a good date
  • Miracle or a trick?
• Exercises

The following sections are included:

• Introduction
• Random Variable
• Probability Distribution
• Laws of Expected Value
• Describing Probability Distributions
  • Mean μ of a probability distribution
    • Toss two coins
    • Sum of two dice
    • Chuck-A-Luck
    • St. Petersburg paradox
    • Monte Carlo
    • Insurance
    • Medical clinic tests
    • Is life fair?
    • Betting odds
  • Variance σ²
  • Standard deviation σ
    • Example 1
    • Example 2
    • Example 3
  • Skewness
  • Kurtosis
• Linear Functions of Random Variables
• Joint Probability Distributions
  • Covariance
    • Lakers and Kings
    • Guilty and convicted
  • Correlation coefficient
    • Lakers and Kings
    • Guilty and convicted
• Linear Functions
  • Restaurant example
  • Shiller example
  • Sample mean example
  • Hedge fund example
• Cumulative Distribution Functions
• Summation Sign Notes
• Exercises

The following sections are included:

• Introduction
• Discrete Probability Distributions
  • Bernoulli trial probability distribution
  • Binomial probability distribution
    • Shape of a binomial distribution
    • Examples
  • The Poisson distribution
    • Examples
• Continuous Probability Distributions
  • Uniform probability distribution
  • From binomial to the normal
  • The normal distribution
    • Standardized normal random variable
    • Examples
  • The exponential distribution
    • Examples
  • Chi-Square distribution
  • The Student’s t-distribution
  • The F-distribution
  • Cauchy distribution
• Exercises

The following sections are included:

• Introduction
• Random Sample
• Statistical Inference
• Properties of Estimators
  • Unbiasedness
  • Consistency
  • Efficiency
  • Mean squared error
• The Sampling Distribution of the Sample Mean
  • Law of Large Numbers
  • Sampling distribution of the sample mean $\overline{X}$ when X is normally distributed
  • Examples
  • Central limit theorem (1930s)
    • Example
• The Sampling Distribution of the Sample Variance
  • Examples
• The Sampling Distribution of the Population Proportion
  • Examples
• Exercises

The following sections are included:

• Introduction
• Population Mean When We Know the Population Variance
  • Examples
• Population Mean When We Do not Know the Population Variance (the Usual Case)
• Population Variance
• Population Proportion
• Final Thoughts
• Exercises

The following sections are included:

• Introduction
• Types of Errors
• Hypothesis Testing
  • Hypothesis testing procedure
• Testing Hypotheses About the Population Mean When the Population Variance Is Known
• Testing Hypotheses About the Population Mean When the Population Variance Is Unknown
• Testing Hypotheses About the Population Variance
• Testing Hypotheses About the Population Proportion
• Observations
• Exercises

The following sections are included:

• Introduction
• Differences in Two Means
  • Matched pairs
  • Population variances ${\sigma }_x^2$ and ${\sigma }_y^2$ are known
    • Example
    • Note on Group differences vs Individual differences
  • Population variances ${\sigma }_x^2$ and ${\sigma }_y^2$ are unknown
    • Two population variances are the same. ${\sigma }_x^2={\sigma }_y^2$
    • Example
    • Two population variances are different, but sample sizes are really large
    • Example
    • Two population variances are different, but sample sizes are small
    • Example
• Differences in Two Variances
• Differences in Two Population Proportions
  • Example
• Exercises

The following sections are included:

• Introduction
• Regression Analysis
  • Example 1: Random numbers
  • Example 2: Hanford Site
• Point Estimation
  • Notation
• Sampling Distribution
  • Slope estimates
  • Intercept estimate
  • Sampling distribution
• Efficiency
  • Efficiency of slope estimates
  • Efficiency of intercept estimates
• Hypothesis Testing
• Example: Hanford Site II
• Direction of Causality
• Covariance Between the Slope and the Intercept
• Exercises

The following sections are included:

• Introduction
• Notation
• Gauss–Markov
  • Gauss–Markov assumptions
  • Gauss–Markov theorem
• Goodness of Fit
  • Why is the R² called the R²?
• Hypothesis Testing
• Example
• Regression F -Statistic
• F -statistic and the R²
  • Example
• Generalized F-Tests
• Example
• Testing Linear Equality Constraints
  • Single linear equality constraint
  • Multiple linear equality constraints
  • Equality of coefficients across regressions
  • Example
  • Structural difference with small samples
• t-test vs F-test
  • Example
• Linear Algebra
• Exercises

The following sections are included:

• Introduction
• Regression to the Mean
• Functional Forms
• Growth Rates
  • Continuous growth rates
    • Constant continuous growth rates
    • Changing continuous growth rates
  • Discrete growth rates
• Elasticity
• Statistical Significance
• Scaling and Units of Measure
• Beta Star Coefficients
  • Example
• Stepwise Linear Regression
• Common Regression Mistakes
  • Garbage in, garbage out
  • Functional form of the regression equation must be correct
  • Multicollinearity
  • Omitted variable bias
  • Data mining
  • Correlation is not causation
  • Reverse causality
  • Extrapolating beyond the data
  • Please be careful
• Exercises

The following sections are included:

• Appendix
• Index