The purpose of this manual is to present the basic principles of Statistics in a systematic and explanatory way, avoiding specific mathematical difficulties, but also to provide the reader with the ability to familiarize themselves with the use of computers when applying them.
The first two chapters deal with introductory concepts of statistics, specifically descriptive statistics. Understanding these concepts is helpful for easier learning of the concepts in the following chapters.
Chapters 3, 4, and 5 provide a brief introduction to probabilities and study the basic theoretical distributions. An introduction to multidimensional distributions is given in Chapter 6, with an emphasis on the study of independent random variables.
Chapter 7 analyzes the concept of normal approximation as well as its relationship with the broader term of statistical research and sampling. The remaining chapters formulate and develop the basic methods for drawing statistical inferences about the parameters that characterize a population, based on a random sample taken from it. Thus, Chapter 8 presents the necessary technical tools that will help us draw these conclusions.
Chapter 9 develops various methods for estimating the parameters of a population, while in Chapter 10, these estimates are made with the help of Confidence Intervals. Other methods of drawing statistical inferences are those of Hypothesis Testing and are given in Chapter 11.
In Chapters 9, 10, and 11, we always assume that the population under study follows a Normal distribution, something that can be statistically tested. The latter is achieved in Chapter 12 with the help of Goodness-of-Fit Tests. Also, in the same chapter, other statistical problems are developed, such as that of testing the Independence between two qualitative characteristics.
In Chapter 13, with the help of Simple Linear Regression, we study the joint behavior of two variables, estimating the Regression Line, the degree of dependence of the variables, and providing the statistical effectiveness of our conclusions regarding it.
With the basic principles of Analysis of Variance, given in Chapter 14, we compare the means of multiple populations. Chapter 15 is the generalization of Chapter 13 and concerns Multivariate Regression.
Chapter 16 presents the basic principles of Time Series and then briefly presents the Box-Jenkins models for time series. The basic Non-Parametric tests are presented in Chapter 16. All examples and exercises are applications of Statistics, useful for economists and business executives.
Finally, the entire Statistical Methodology developed in the book, along with its examples, is also done using Excel and is presented at the end of the book as an independent chapter titled "Excel User Guide". The writing of Excel was significantly contributed by the graduate of mathematics, Mr. Petridis Kostas, whom I warmly thank.