Teaches all the basic statistical concepts with a minimum of fuss
Includes applications of clear relevance to business and economics
Enhances students´ understanding by focusing on non-trivial problems
Jan Ubøe is a Professor of Mathematics at the Norwegian School of Economics. He has published research in several different areas of mathematics and economics: theory on stochastic differential equations, option pricing theory, regional science, transportation science and management science. His contributions have also been recognized with several awards for excellence in teaching.
This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor.
The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.
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1 Deillegalscriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1 Population and samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 The median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.3 Quartiles and mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4 Relative frequency and histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.5 The mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.6 Sample variance and sample standard deviation . . . . . . . . . . . . . . . . . 21
1.7 Sample covariance and coefficient of variation . . . . . . . . . . . . . . . . . . 23
1.8 Using Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.9 Summary of Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.10 Problems for chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.1 Sample space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1 Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2.2 Uniform probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.2.3 Set theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.4 Computing probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.2.5 The negation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3 Summary of Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Problems for chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 Combinatorics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1 Counting combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.1.1 Ordered selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.1.2 Unordered choices without replacement . . . . . . . . . . . . . . . . . 54
3.1.3 Combinatorial probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Summary of Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3 Problems for chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Conditional probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1 Conditional probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.1.1 Computing conditional probabilities . . . . . . . . . . . . . . . . . . . . 67
4.1.2 Splitting the sample space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.3 Probability trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Subjective probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.4 Summary of Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.5 Problems for chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5 Random variables, mean and variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.2.1 Computing expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.2.2 General expectations and variance . . . . . . . . . . . . . . . . . . . . . . 94
5.3 Some simple facts about option pricing . . . . . . . . . . . . . . . . . . . . . . . . 96
5.3.1 Hedging portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.4 Summary of Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.5 Problems for chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6 Joint distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1 Simultaneous distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.2.1 An alternative formula for the covariance . . . . . . . . . . . . . . . . 115
6.2.2 Sums of random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.3 Summary of Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.4 Problems for chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 Basic probability distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.1 The indicator distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7.2 The binomial distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3 The hypergeometric distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
7.4 The Poisson distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.5 The normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.5.1 The general normal distribution . . . . . . . . . . . . . . . . . . . . . . . . 138
7.5.2 Standardizing random variables . . . . . . . . . . . . . . . . . . . . . . . . 139
7.5.3 The central limit theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.5.4 Integer correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.5.5 Normal approximation of hypergeometric and Poisson
distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.5.6 Summing normal distributions . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.5.7 Applications to option pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.6 Summary of chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.7 Problems for chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
8 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1.1 Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.1.2 Reporting estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.1.3 The measurement model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.2 Confidence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
8.2.1 Constructing confidence intervals . . . . . . . . . . . . . . . . . . . . . . . 174
8.2.2 The t-distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
8.3 The lottery model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8.4 Summary of Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
8.5 Problems for chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
9.1 Basic ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
9.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
9.3 General principles for hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . 189
9.4 Designing statical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
9.4.1 One-sided and two-sided tests . . . . . . . . . . . . . . . . . . . . . . . . . . 195
9.4.2 Confidence intervals and hypothesis testing . . . . . . . . . . . . . . 196
9.4.3 P-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
9.5 Summary of Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9.6 Problems for chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
10 Commonly used tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
10.1 Testing binomial distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
10.2 t-test for expected value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
10.3 Comparing two groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
10.3.1 t-test for comparison of expectation in two groups . . . . . . . . . 215
10.3.2 t-test executed in Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
10.3.3 t-test for comparison of expectation in two groups, paired
observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
10.3.4 t-test with paired observations executed in Excel . . . . . . . . . . 222
10.4 Wilcoxon´s distribution free tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
10.4.1 The Wilcoxon signed-rank test . . . . . . . . . . . . . . . . . . . . . . . . . 225
10.4.2 Comparison of t-tests and Wilcoxon test . . . . . . . . . . . . . . . . . 227
10.5 The U-test for comparison of success probabilities . . . . . . . . . . . . . . . 228
10.6 Chi-square test for goodness-of-fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
10.6.1 The Chi-square test executed in Excel . . . . . . . . . . . . . . . . . . . 232
10.7 The Chi-square test for independence . . . . . . . . . . . . . . . . . . . . . . . . . . 233
10.7.1 The Chi-square test for independence executed in Excel . . . . 236
10.8 Summary of Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
10.9 Problems for chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
10 Contents
11 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
11.1 Linear correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
11.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
11.3 Residuals and explanatory power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
11.3.1 Naming variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
11.4 Hypothesis testing in the regression model . . . . . . . . . . . . . . . . . . . . . 261
11.5 Prediction/estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
11.6 Regression using Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
11.7 Multiple regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
11.7.1 Explanatory power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
11.8 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
11.9 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
11.10 Dummy variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
11.11 Analyzing residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
11.11.1 Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
11.11.2 Normal score plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
11.11.3 Residuals in observed order . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
11.11.4 Residuals sorted with respect to size . . . . . . . . . . . . . . . . . . . . 277
11.12 Summary of Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.13 Problems for chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor.
The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.
"This textbook is an introductory one which is intended first of all for researchers, analysts and practitioners in finance and economics which are not going to become professional statisticians. ... the author introduces the readers to the complex technology through many examples and exercises which are simple and explicit at the beginning and grow up to nontrivial problems of economic practice.” (Vladimir Gorbunov, zbMATH 1407.62008, 2019)
This textbook discusses central statistical concepts and their use in business and economics. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The book bridges the gap between theory and applications, with most exercises formulated in an economic context.
This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor.
The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.
Introduction.- Deillegalscriptive statistics.- Probability.- Combinatorics.- Conditional probability.- Random variables, mean and variance.- Joint distributions.- Basic probability distributions.- Estimation.- Hypothesis testing.- Commonly used tests.- Linear regression.- Solutions.
"This textbook is an introductory one which is intended first of all for researchers, analysts and practitioners in finance and economics which are not going to become professional statisticians. ... the author introduces the readers to the complex technology through many examples and exercises which are simple and explicit at the beginning and grow up to nontrivial problems of economic practice." (Vladimir Gorbunov, zbMATH 1407.62008, 2019)
Über den Autor
Jan Ubøe is a Professor of Mathematics at the Norwegian School of Economics. He has published research in several different areas of mathematics and economics: theory on stochastic differential equations, option pricing theory, regional science, transportation science and management science. His contributions have also been recognized with several awards for excellence in teaching.
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Inhaltsverzeichnis
1 Deillegalscriptive statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.1 Population and samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 The median . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3 Quartiles and mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.4 Relative frequency and histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181.5 The mean . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191.6 Sample variance and sample standard deviation . . . . . . . . . . . . . . . . . 211.7 Sample covariance and coefficient of variation . . . . . . . . . . . . . . . . . . 231.8 Using Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.9 Summary of Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.10 Problems for chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.1 Sample space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2.1 Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.2.2 Uniform probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.2.3 Set theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.2.4 Computing probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.2.5 The negation principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.3 Summary of Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452.4 Problems for chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 Combinatorics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.1 Counting combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.1.1 Ordered selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.1.2 Unordered choices without replacement . . . . . . . . . . . . . . . . . 543.1.3 Combinatorial probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2 Summary of Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.3 Problems for chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594 Conditional probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1 Conditional probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.1.1 Computing conditional probabilities . . . . . . . . . . . . . . . . . . . . 674.1.2 Splitting the sample space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1.3 Probability trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.2 Subjective probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.4 Summary of Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.5 Problems for chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775 Random variables, mean and variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.1 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2 Expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.2.1 Computing expectations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.2.2 General expectations and variance . . . . . . . . . . . . . . . . . . . . . . 945.3 Some simple facts about option pricing . . . . . . . . . . . . . . . . . . . . . . . . 965.3.1 Hedging portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.4 Summary of Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.5 Problems for chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006 Joint distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.1 Simultaneous distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.2 Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1146.2.1 An alternative formula for the covariance . . . . . . . . . . . . . . . . 1156.2.2 Sums of random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166.3 Summary of Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.4 Problems for chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1187 Basic probability distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257.1 The indicator distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257.2 The binomial distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1267.3 The hypergeometric distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1297.4 The Poisson distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337.5 The normal distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1357.5.1 The general normal distribution . . . . . . . . . . . . . . . . . . . . . . . . 1387.5.2 Standardizing random variables . . . . . . . . . . . . . . . . . . . . . . . . 1397.5.3 The central limit theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1407.5.4 Integer correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1457.5.5 Normal approximation of hypergeometric and Poissondistributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1477.5.6 Summing normal distributions . . . . . . . . . . . . . . . . . . . . . . . . . 1487.5.7 Applications to option pricing . . . . . . . . . . . . . . . . . . . . . . . . . . 1487.6 Summary of chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1507.7 Problems for chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1528 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1698.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1698.1.1 Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1708.1.2 Reporting estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1728.1.3 The measurement model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1728.2 Confidence intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1738.2.1 Constructing confidence intervals . . . . . . . . . . . . . . . . . . . . . . . 1748.2.2 The t-distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1768.3 The lottery model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1798.4 Summary of Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1808.5 Problems for chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1819 Hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1859.1 Basic ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1859.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1879.3 General principles for hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . 1899.4 Designing statical tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1919.4.1 One-sided and two-sided tests . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.4.2 Confidence intervals and hypothesis testing . . . . . . . . . . . . . . 1969.4.3 P-value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.5 Summary of Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2009.6 Problems for chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20110 Commonly used tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110.1 Testing binomial distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110.2 t-test for expected value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21310.3 Comparing two groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21510.3.1 t-test for comparison of expectation in two groups . . . . . . . . . 21510.3.2 t-test executed in Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21810.3.3 t-test for comparison of expectation in two groups, pairedobservations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21910.3.4 t-test with paired observations executed in Excel . . . . . . . . . . 22210.4 Wilcoxon's distribution free tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22210.4.1 The Wilcoxon signed-rank test . . . . . . . . . . . . . . . . . . . . . . . . . 22510.4.2 Comparison of t-tests and Wilcoxon test . . . . . . . . . . . . . . . . . 22710.5 The U-test for comparison of success probabilities . . . . . . . . . . . . . . . 22810.6 Chi-square test for goodness-of-fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23110.6.1 The Chi-square test executed in Excel . . . . . . . . . . . . . . . . . . . 23210.7 The Chi-square test for independence . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.7.1 The Chi-square test for independence executed in Excel . . . . 23610.8 Summary of Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23610.9 Problems for chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23710 Contents11 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25311.1 Linear correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25311.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25511.3 Residuals and explanatory power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25811.3.1 Naming variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26011.4 Hypothesis testing in the regression model . . . . . . . . . . . . . . . . . . . . . 26111.5 Prediction/estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26411.6 Regression using Excel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26711.7 Multiple regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26911.7.1 Explanatory power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26911.8 Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27111.9 Multicollinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27211.10 Dummy variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27311.11 Analyzing residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27511.11.1 Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27511.11.2 Normal score plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27511.11.3 Residuals in observed order . . . . . . . . . . . . . . . . . . . . . . . . . . . 27611.11.4 Residuals sorted with respect to size . . . . . . . . . . . . . . . . . . . . 27711.12 Summary of Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27811.13 Problems for chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
Klappentext
This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor.
The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.
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