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Introductory Statistics for Business and Economics Jan Uboe

Introductory Statistics for Business and Economics By Jan Uboe

Introductory Statistics for Business and Economics by Jan Uboe


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Summary

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.

Introductory Statistics for Business and Economics Summary

Introductory Statistics for Business and Economics: Theory, Exercises and Solutions by Jan Uboe

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.


Introductory Statistics for Business and Economics Reviews

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)

About Jan Uboe

Jan Uboe 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.

Table of Contents

1 Descriptive 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

Additional information

NLS9783319890166
9783319890166
3319890166
Introductory Statistics for Business and Economics: Theory, Exercises and Solutions by Jan Uboe
New
Paperback
Springer International Publishing AG
2019-06-06
466
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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