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#### Document Type

Book

#### Description

**Preface & Acknowledgments**

This textbook is designed for a higher level undergraduate, perhaps even first year graduate, course for engineering or science students who are interested to gain knowledge of using data analysis to make predictive models. While there is no statistical perquisite knowledge required to read this book, due to the fact that the study is designed for the reader to truly understand the underlying theory rather than just learn how to read computer output, it would be best read with some familiarity of elementary statistics. The book is self-contained and the only true perquisite knowledge is a solid understanding of university level calculus, which of course it is expected that any engineering or science student will have mastery off. The intention for this textbook is for an elective type course; however, the foundations are laid here for further mathematical study and this text could well serve as a transition for an interested student with little to no prior knowledge to then go on to study in the popular fields of data scientist, big data or whatever the buzz words of the day may call it. A natural next read would be something equivalent to the popular texts “an introduction to statistical learning” or the “the elements of statistical learning,” by Hastie & Friedman et al.

The author is very grateful for the opportunity to have implemented and taught the MA 413 course at his current institution, Embry Riddle Aeronautical University in Daytona Beach, Fl. It was that course which led to me writing this textbook evolving for class notes, and I am very thankful to the many students who made corrections along the way. And, of course I am extremely grateful to my wife who supported me & encouraged me to labor on, hence I dedicate this book to her!

#### Contents

**Ch 1 Introduction **

** 1.1 "review of descriptive statistics" page 4**

** 1.2 "introduction to correlation & regression" page 11**

**Ch 2 Overview of Probability Theory**

** 2.1 "continuous random variables" page 20**

** 2.2 "introduction to density functions" page 23**

** 2.3 "expectation and variance" page 31**

**Ch 3 General Linear Model**

** 3.1 "foundational theory of hypothesis testing" page 38**

** 3.2 "introduction to the general linear model" page 45**

** 3.3 "one way ANOVA and the F test" page 49**

** 3.4 "single variable linear regression" page 57**

** 3.5 "examples of single variable regression" page 66**

** 3.6 "ANOVA error analysis for regression" page 70**

** 3.7 "multivariable linear regression" page 82**

** 3.9 "a brief introduction to model optimization" page 96**

**Ch 4 Applications to financial modeling**

** 4.1 "introduction and definition of volatility" page 103**

** 4.2 "a macro economic model & suggested further study" page 113**

#### Publication Date

2019

#### Course Number

MA 413

#### Course Title

Statistics

#### Disciplines

Mathematics | Statistics and Probability

#### Scholarly Commons Citation

Smith, Tim, "A Self-Contained Course in the Mathematical Theory of Statistics for Scientists & Engineers with an Emphasis On Predictive Regression Modeling & Financial Applications." (2019). *Open Access Textbooks*. 5.

https://commons.erau.edu/oer-textbook/5

#### Copyright Information

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License