Business Statistics with Solutions in R (eBook)

lt;p> Mustapha Abiodun Akinkunmi, associate professor of finance and chair of the accounting and finance department at the American University of Nigeria, Yola, Nigeria, is a financial economist and technology strategist with over 25 years of experience in estimation, planning, and forecasting using statistical and econometric methods, with particular expertise in risk, expected utility, discounting, binomial-tree valuation methods, financial econometrics models, Monte Carlo simulations, macroeconomics, and exchange rate modeling. Dr. Akinkunmi has performed extensive software development for quantitative analysis of capital markets, revenue and payment gateway, predictive analytics, data science, and credit risk management. He has worked as a business strategist with AT&T, Salomon Brothers, Goldman Sachs, Phibro Energy, First Boston (Credit Suisse First Boston), World Bank, and Central Bank of Nigeria. He has taught and researched at Manhattan College, Riverdale, NY; Fordham University, New York, NY; University of Lagos, Lagos, Nigeria; State University of New York-FIT, New York, NY; Montclair State University, Montclair, NJ; and American University, Yola, Nigeria. In 1990, he founded Technology Solutions Incorporated (TSI) in New York, which focused on data science and software application development for clients including major financial services institutions. Dr. Akinkunmi is the former Honorable Commissioner for Finance, Lagos State, Nigeria.

Chapter One: Introduction to Statistical Analysis

1.1 Scale of measurement

1.2 Data, data collection and presentation

1.3 Data grouping

1.4 Methods of visualizing data

1.5 Introduction to R software

Chapter Two: Descriptive Data

Chapter One: Introduction to Statistical Analysis

Scale of measurement

Data, data collection and presentation

Data grouping

Methods of visualizing data

Introduction to R software

Chapter Two: Descriptive Data

2.1. Measure of Central tendency

2.2. Measure of Dispersion

2.3. Shapes of the distribution—symmetric and asymmetric

2.4. Summary statistics of data using R

Chapter Three: Basic Probability Concepts

3.1. Experiment and sample space

3.2. Elementary events

3.3 Venn diagram and probability matrices for two sets probability problems.

3.4 Addition rule of probability

3.5 Independent events and dependent events.

3.6 Multiplication rule of probability

3.7 Conditional probabilities

Chapter Four: Discrete Probability Distributions

4.1. Expected value and variance of a discrete random variable

4.2. Binomial probability distribution

4.3. Expected value and variance of a binomial distribution

4.4. Solve problems involving binomial distribution using R

Chapter Five: Continuous Probability Distribution

5.1. Normal distribution and standardized normal distribution

5.2. Normal curve

5.3. Approximate normal to the binomial distribution

5.4. Use of the normal distribution in business problem solving using R

Chapter Six: Sampling and Sampling Distribution

6.1. Probability and non-probability sampling

6.2. Sampling techniques- simple random, systematic, stratified, and cluster samples

6.3. Sampling distribution of the mean

6.4. Central limit theorem and its significance

Chapter Seven: Confidence Intervals for Single Population Mean and Proportion

7.1. Point estimates and interval estimates

7.2. Confidence intervals for mean and proportion

7.3. Confidence interval for proportion

7.4 Factors that determine margin of error

Chapter Eight: Hypothesis Testing for Single Population Mean and Proportion

8.1. Null and alternative hypotheses

8.2 Type I and Type II Error

8.3. Acceptance and Rejection regions

8.4. Hypothesis testing procedure

Chapter Nine: Regression Analysis and Correlation

9.1. Construction of line fit plots

9.2. Types of regression analysis

9.2.1 Uses of regression analysis

9.2.2 Simple linear regression

9.2.3 Assumptions of simple linear regression

9.3. Multiple linear regression

9.3.1 Significance testing of each variable

9.3.2. Interpretation of regression coefficients and other output

9.4 Pearson correlation coefficient

9.4.1 Assumptions of correlation test

9.4.2 Types of correlation

9.4.3 Coefficient of determination

9.4.4 Test for the significance of correlation coefficient (r)

Chapter Ten: Poisson Distribution

10.1. Poisson distribution and its properties

10.2. Mean and variance of a Poisson distribution

10.3. Application of Poisson distribution

10.4. Poisson to approximate the Binomial

Chapter Eleven: Uniform Distribution

11.1. Uniform distribution and its properties

11.2. Mean and variance of a uniform distribution

11.3. Application of uniform distribution

Chapter Twelve: Statistical Process Control

12.1. Types of control chart

12.2 Uses of control chart

12.3 Procedure of control chart

12.4. Variable control charts

12.4.1. X-bar chart

12.4.1.1. Steps for constructing X-bar chart

12.4.2. Range chart

12.4.2.1. Steps for constructing R-chart

12.4.3. S-chart

12.4.4. NP chart

12.4.5. P chart

12.4.6. C chart

12.4.7. U chart

Chapter Thirteen: Time Series

13.1. Concept of Time series data

13.1.1 Uses and application of time series analysis

13.2 Univariate time series model

13.2.1 Generating a time-series object in R

13.2.2. Smoothing and seasonal decomposition

13.2.2.3. Exponential Forecasting Models

13.2.2.4. Holt and Holt-Winters exponential smoothing

13.2.2.5 The ets( ) function and automated forecasting

13.2.2.5. ARIMA forecasting models

13.3 Multivariate time series model

13.3.1. ARMA and ARIMA models

13.4 Recap

Chapter Fourteen: Multivariate Analysis

14.1. Properties of Multivariate Normal Distribution

14.2. Sampling from a Multivariate Normal Distribution and Maximum Likelihood Estimation

14.2.1. Multivariate Normal Distribution

14.2.2 Maximum Likelihood Estimation of Mean (μ) and Covariance matrix (Σ)

14.3 The Sampling Distribution X ̅ and

14.3.1 Wishart Distribution

14.3.2 Properties of the Wishart Distribution

14.3.3 Large Sample Properties of X ̅ and

14.4 Multivariate Normality

14.4.1 Q-Q Plot for Evaluating Multivariate Normality

14.4.1.1 Steps for Constructing Chi-squared plot

Chapter Fifteen: Inference About a Mean Vector

15.1 Test of Hypothesis [μ=μ_0]

15.2 Confidence Interval and Simultaneous Comparison of Component Means

15.2.1 Confidence Regions

15.2.2 Simultaneous Confidence Intervals

15.2.3 Bonferroni Method of Multiple Comparisons

15.2.3 Large Sample Inference about a Population Mean Vector

15.2.4 Multivariate Quality Control Charts

15.2.4.1 Univariate Case

15.2.4.1 Multivariate Case

Chapter Sixteen: Inference About a Mean Vector

16.1 Paired Comparisons

16.2 Repeated Measurement Comparisons

16.3 Comparisons of Mean Vectors from Two Populations

16.4 Several Multivariate Population Means Comparison.

16.4.1 Univariate Analysis of Variance (ANOVA)

16.4.1.1 Assumptions of ANOVA

16.4.2 Multivariate Analysis of Variance (MANOVA)

16.4.2.1 Assumptions of MANOVA