Statistics for Economists

✍ Scribed by Linus Yamane

• Publisher: World Scientific
• Year: 2024
• Tongue: English
• Leaves: 373
• Category: Library

✦ Synopsis

This first course in statistics is designed for undergraduate students. There are dozens of statistics textbooks in the market. But most of these textbooks are either pitched at a level that is too high or too low for most undergraduate students. Many use calculus and are designed for graduate students in technical fields. Others provide black box formulas without any derivations. This textbook focuses on deriving everything from first principles without using calculus or linear algebra. It is important for students to understand why they are doing what they are doing. Otherwise students cannot distinguish meaningless results from significant results. This textbook gets to the major points quickly and is thus relatively short and very accessible.

✦ Table of Contents

Contents
Preface
About the Author
Acknowledgements
Chapter 1 Why Statistics?
1.1 Introduction
1.2 Goals
1.2.1 Think more clearly
1.2.2 Understand uncertainty
1.2.3 Understand the world
1.2.4 Make decisions under uncertainty
1.3 Who Should I Marry?
1.4 Is Statistics Hard?
1.5 Are Americans in Love?
1.6 Population
1.7 Sample
1.8 Goals
1.9 Exercises
Chapter 2 Descriptive Statistics
2.1 Introduction
2.2 Descriptive Statistics
2.3 Inferential Statistics
2.4 Variables
2.5 Describing Variables
2.6 Graphing Data
2.6.1 Pie charts and bar graphs
2.6.2 Stem plots
2.6.3 Histograms
2.6.4 Time series plots
2.7 Numerical Summaries
2.7.1 Center of a distribution
2.7.2 Spread of a distribution
2.8 Linear Transformations
2.9 Relationships
2.10 Quantitative Data
2.10.1 Scatterplot of X and Y
2.10.2 Covariance
2.10.3 Correlation coefficient
2.10.4 Correlation ≠ causality
2.11 Qualitative Data
2.11.1 Simpson’s paradox
2.12 Exercises
Chapter 3 Probability
3.1 Introduction
3.2 Classical Probability
3.3 Frequentist Probability
3.4 Subjective Probability
3.5 Back to Classical Probability
3.5.1 Ordering n distinct items
3.5.2 Permutations of x out of n distinct items
3.5.3 Combinations of x out of n distinct items
3.6 Rules of Probability
3.6.1 Conditional probability
3.7 The Addition Rule
3.7.1 Example
3.8 The Multiplication Rule
3.8.1 Examples
3.9 The Subtraction Rule
3.10 Some Examples
3.10.1 Some birthdays vs particular birthdays
3.10.2 Julius Caesar and you
3.11 Bayes Theorem
3.11.1 Lizzie Borden
3.11.2 HIV/AIDS?
3.11.3 Subjective probability of having a good date
3.11.4 Miracle or a trick?
3.12 Exercises
Chapter 4 Probability Distributions
4.1 Introduction
4.2 Random Variable
4.3 Probability Distribution
4.4 Laws of Expected Value
4.5 Describing Probability Distributions
4.5.1 Mean μ of a probability distribution
4.5.1.1 Toss two coins
4.5.1.2 Sum of two dice
4.5.1.3 Chuck-A-Luck
4.5.1.4 St. Petersburg paradox
4.5.1.5 Monte Carlo
4.5.1.6 Insurance
4.5.1.7 Medical clinic tests
4.5.1.8 Is life fair?
4.5.1.9 Betting odds
4.5.2 Variance σ2
4.5.3 Standard deviation σ
4.5.3.1 Example 1
4.5.3.2 Example 2
4.5.3.3 Example 3
4.5.4 Skewness
4.5.5 Kurtosis
4.6 Linear Functions of Random Variables
4.7 Joint Probability Distributions
4.7.1 Covariance
4.7.1.1 Lakers and Kings
4.7.1.2 Guilty and convicted
4.7.2 Correlation coefficient
4.7.2.1 Lakers and Kings
4.7.2.2 Guilty and convicted
4.8 Linear Functions
4.8.1 Restaurant example
4.8.2 Shiller example
4.8.3 Sample mean example
4.8.4 Hedge fund example
4.9 Cumulative Distribution Functions
4.10 Summation Sign Notes
4.11 Exercises
Chapter 5 Special Probability Distributions
5.1 Introduction
5.2 Discrete Probability Distributions
5.2.1 Bernoulli trial probability distribution
5.2.2 Binomial probability distribution
5.2.2.1 Shape of a binomial distribution
5.2.2.2 Examples
5.2.3 The Poisson distribution
5.2.3.1 Examples
5.3 Continuous Probability Distributions
5.3.1 Uniform probability distribution
5.3.2 From binomial to the normal
5.3.3 The normal distribution
5.3.3.1 Standardized normal random variable
5.3.3.2 Examples
5.3.4 The exponential distribution
5.3.4.1 Examples
5.3.5 Chi-Square distribution
5.3.6 The Student’s t-distribution
5.3.7 The F-distribution
5.3.8 Cauchy distribution
5.4 Exercises
Chapter 6 Statistical Inference: Sampling and Sampling Distributions
6.1 Introduction
6.2 Random Sample
6.3 Statistical Inference
6.4 Properties of Estimators
6.4.1 Unbiasedness
6.4.2 Consistency
6.4.3 Efficiency
6.4.4 Mean squared error
6.5 The Sampling Distribution of the Sample Mean
6.5.1 Law of Large Numbers
6.5.2 Sampling distribution of the sample mean X when X is normally distributed
6.5.3 Examples
6.5.4 Central limit theorem (1930s)
6.5.4.1 Example
6.6 The Sampling Distribution of the Sample Variance
6.6.1 Examples
6.7 The Sampling Distribution of the Population Proportion
6.7.1 Examples
6.8 Exercises
Chapter 7 Confidence Intervals
7.1 Introduction
7.2 Population Mean When We Know the Population Variance
7.2.1 Examples
7.3 Population Mean When We Do not Know the Population Variance (the Usual Case)
7.4 Population Variance
7.5 Population Proportion
7.6 Final Thoughts
7.7 Exercises
Chapter 8 Hypothesis Testing
8.1 Introduction
8.2 Types of Errors
8.3 Hypothesis Testing
8.3.1 Hypothesis testing procedure
8.4 Testing Hypotheses About the Population Mean When the Population Variance Is Known
8.5 Testing Hypotheses About the Population Mean When the Population Variance Is Unknown
8.6 Testing Hypotheses About the Population Variance
8.7 Testing Hypotheses About the Population Proportion
8.8 Observations
8.9 Exercises
Chapter 9 Hypothesis Testing with Two Samples
9.1 Introduction
9.2 Differences in Two Means
9.2.1 Matched pairs
9.2.2 Population variances σ2x and σ2y are known
9.2.2.1 Example
9.2.2.2 Note on Group differences vs Individual differences
9.2.3 Population variances σ2x and σ2y are unknown
9.2.3.1 Two population variances are the same σ2x = σ2
9.2.3.2 Example
9.2.3.3 Two population variances are different, but sample sizes are really large
9.2.3.4 Example
9.2.3.5 Two population variances are different, but sample sizes are small
9.2.3.6 Example
9.3 Differences in Two Variances
9.4 Differences in Two Population Proportions
9.4.1 Example
9.5 Exercises
Chapter 10 Simple Regression
10.1 Introduction
10.2 Regression Analysis
10.2.1 Example 1: Random numbers
10.2.2 Example 2: Hanford Site
10.3 Point Estimation
10.3.1 Notation
10.4 Sampling Distribution
10.4.1 Slope estimates
10.4.2 Intercept estimate
10.4.3 Sampling distribution
10.5 Efficiency
10.5.1 Efficiency of slope estimates
10.5.2 Efficiency of intercept estimates
10.6 Hypothesis Testing
10.7 Example: Hanford Site II
10.8 Direction of Causality
10.9 Covariance Between the Slope and the Intercept
10.10 Exercises
Chapter 11 Multiple Regression
11.1 Introduction
11.2 Notation
11.3 Gauss–Markov
11.3.1 Gauss–Markov assumptions
11.3.2 Gauss–Markov theorem
11.4 Goodness of Fit
11.4.1 Why is the R2 called the R2?
11.5 Hypothesis Testing
11.6 Example
11.7 Regression F-Statistic
11.8 F-statistic and the R2
11.8.1 Example
11.9 Generalized F-Tests
11.10 Example
11.11 Testing Linear Equality Constraints
11.11.1 Single linear equality constraint
11.11.2 Multiple linear equality constraints
11.11.3 Equality of coefficients across regressions
11.11.4 Example
11.11.5 Structural difference with small samples
11.12 t-test vs F-test
11.12.1 Example
11.13 Linear Algebra
11.14 Exercises
Chapter 12 Interpreting Regression Results
12.1 Introduction
12.2 Regression to the Mean
12.3 Functional Forms
12.4 Growth Rates
12.4.1 Continuous growth rates
12.4.1.1 Constant continuous growth rates
12.4.1.2 Changing continuous growth rates
12.4.2 Discrete growth rates
12.5 Elasticity
12.6 Statistical Significance
12.7 Scaling and Units of Measure
12.8 Beta Star Coefficients
12.8.1 Example
12.9 Stepwise Linear Regression
12.10 Common Regression Mistakes
12.10.1 Garbage in, garbage out
12.10.2 Functional form of the regression equation must be correct
12.10.3 Multicollinearity
12.10.4 Omitted variable bias
12.10.5 Data mining
12.10.6 Correlation is not causation
12.10.7 Reverse causality
12.10.8 Extrapolating beyond the data
12.10.9 Please be careful
12.11 Exercises
Appendix
Index