Statistics.For.Economists

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