Good data analytics is the basis for effective decisions. Whoever has the data, has the ability to extract information promptly and effectively to make pertinent decisions. The premise of this handbook is to empower users and tool developers with the appropriate collection of formulas and techniques for data analytics and to serve as a quick reference to keep pertinent formulas within fingertip reach of readers.
This handbook includes formulas that will appeal to mathematically inclined readers. It discusses how to use data analytics to improve decision-making and is ideal for those new to using data analytics to show how to expand their usage horizon. It provides quantitative techniques for modeling pandemics, such as COVID-19. It also adds to the suite of mathematical tools for emerging technical areas.
This handbook is a handy reference for researchers, practitioners, educators, and students in areas such as industrial engineering, production engineering, project management, civil engineering, mechanical engineering, technology management, and business management worldwide.
Author(s): Adedeji B. Badiru
Series: Systems Innovation Book Series
Publisher: CRC Press
Year: 2020
Language: English
Pages: 272
City: Boca Raton
Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Acknowledgments
Author
Chapter 1 Essentials of Data Analytics
Introduction to COVID-19 Data Analytics
Systems View of Data Analytics
Global Growth of Data Analytics
Background in Predictive Analytics
Data Modeling Approaches
Data Fanaticism
Data and Measurements for Data Analytics
What is Measurement?
Data Measurement Systems
Fundamental Scientific Equations
Einstein’s Equation
Einstein’s Field Equation
Heisenberg’s Uncertainty Principle
Schrödinger Equation
Dirac Equation
Maxwell’s Equations
Boltzmann’s Equation for Entropy
Planck–Einstein Equation
Planck’s Blackbody Radiation Formula
Hawking Equation for Black Hole Temperature
Navier–Stokes Equation for a Fluid
Lagrangian for Quantum Chromodynamics
Bardeen–Cooper–Schrieffer Equation for Superconductivity
Josephson Effect
Fermat’s Last Theorem
Methods for Data Measurement and Comparison
Direct Comparison
Indirect Comparison
Data Measurement Scales
Nominal Scale of Measurement
Ordinal Scale of Measurement
Interval Scale of Measurement
Ratio Scale Measurement
Reference Units of Measurements
Common Constants
Numeric Data Representation
The Language of Data Analytics
Quick Reference for Mathematical Equations
Reference
Chapter 2 Empirical Model Building
Introduction to the Model Environment
State-Space Modeling
Calculus Reference for Data Analytics
Integration Rules
Solving Integrals with Variable Substitution
Riemann Integral
Integration by Parts
Compound Functions Where the Inner Function is ax
Integration by Parts
Systems Modeling for Data Analytics
Triple C Questions
Communication
Cooperation
Coordination
Conflict Resolution in Data Analytics
References
Chapter 3 Data Visualization Methods
Introduction to Data Visualization
Case Example of “Covidvisualizer” Website
Dynamism and Volatility of Data
Data Determination and Collection
Choosing the Data
Collecting the Data
Relevance Check
Limit Check
Critical Value
Coding the Data
Processing the Data
Control Total
Consistency Check
Scales of Measurement
Using the Information
Data Exploitation
Raw Data
Total Revenue
Average Revenue
Median Revenue
Quartiles and Percentiles
The Mode
Range of Revenue
Average Deviation
Sample Variance
Standard Deviation
Chapter 4 Basic Mathematical Calculations for Data Analytics
Introduction to Calculation for Data Analytics
Quadratic Equation
Overall Mean
Chebyshev’s Theorem
Permutations
Combinations
Failure
Probability Distribution
Probability
Distribution Function
Expected Value
Variance
Binomial Distribution
Poisson Distribution
Mean of a Binomial Distribution
Variance
Normal Distribution
Cumulative Distribution Function
Population Mean
Standard Error of the Mean
t-Distribution
Chi-Squared Distribution
Definition of Set and Notation
Set Terms and Symbols
Venn Diagrams
Operations on Sets
De Morgan’s Laws
Probability Terminology
Basic Probability Principles
Random Variable
Mean Value xˆ or Expected Value
Series Expansions
Mathematical Signs and Symbols
Greek Alphabet
Algebra
Laws of Algebraic Operations
Special Products and Factors
Powers and Roots
Proportion
Arithmetic Mean of n Quantities A
Geometric Mean of n Quantities G
Harmonic Mean of n Quantities H
Generalized Mean
Solution of Quadratic Equations
Solution of Cubic Equations
Trigonometric Solution of the Cubic Equation
Solution of Quadratic Equations
Partial Fractions
Non-repeated Linear Factors
Repeated Linear Factors
General Terms
Repeated Linear Factors
Factors of Higher Degree
Geometry
Triangles
Right Triangle
Equilateral Triangle
General Triangle
Menelaus’s Theorem
Ceva’s Theorem
Quadrilaterals
Rectangle
Parallelogram
Rhombus
Trapezoid
General Quadrilateral
Regular Polygon of n Sides Each of Length b
Regular Polygon of n Sides Inscribed in a Circle of Radius r
Regular Polygon of n Sides Circumscribing a Circle of Radius r
Cyclic Quadrilateral
Prolemy’s Theorem
Cyclic-Inscriptable Quadrilateral
Planar Areas by Approximation
Trapezoidal Rule
Durand’s Rule
Simpson’s Rule (n even)
Weddle’s Rule (n = 6)
Solids Bounded by Planes
Cube
Rectangular Parallelepiped (or Box)
Prism
Pyramid
Prismatoid
Regular Polyhedra
Sphere of Radius r
Right Circular Cylinder of Radius r and Height h
Circular Cylinder of Radius r and Slant Height l
Cylinder of Cross-Sectional Area A and Slant Height l
Right Circular Cone of Radius r and Height h
Spherical Cap of Radius rand Height h
Frustum of Right Circular Cone of Radii a, b and Height h
Zone and Segment of Two Bases
Lune
Spherical Sector
Spherical Triangle and Polygon
Spheroids
Ellipsoid
Oblate Spheroid
Prolate Spheroid
Circular Torus
Formulas from Plane Analytic Geometry
Distance d between Two Points
Slope m of Line Joining Two Points
Equation of Line Joining Two Points
Equation of Line in Terms of x Intercept a ≠ 0 and y intercept b ≠ 0
Normal Form for Equation of Line
General Equation of Line
Distance from Point (x[sub(1)], y[sub(1)]) to Line Ax + By + C = 0
Angle ψ between Two Lines Having Slopes m[sub(1)] and m[sub(2)]
Area of Triangle with Verticles
Transformation of Coordinates Involving Pure Translation
Transformation of Coordinates Involving Pure Rotation
Transformation of Coordinates Involving Translation and Rotation
Polar Coordinates (r,θ)
Plane Curves
Catenary, Hyperbolic Cosine
Cardioid
Circle
Cassinian Curves
Cotangent Curve
Cubical Parabola
Cosecant Curve
Cosine Curve
Ellipse
Gamma Function
Hyperbolic Functions
Inverse Cosine Curve
Inverse Sine Curve
Inverse Tangent Curve
Logarithmic Curve
Parabola
Cubical Parabola
Tangent Curve
Ellipsoid
Elliptic Cone
Elliptic Cylinder
Hyperboloid of One Sheet
Elliptic Paraboloid
Hyperboloid of Two Sheets
Hyperbolic Paraboloid
Sphere
Distance d between Two Points
Equations of Line Joining P[sub(1)](x[sub(1)], y[sub(1)], z[sub(1)]) and P[sub(2)](x[sub(2)], y[sub(2)], z[sub(2)]) in Standard Form
Equations of Line Joining P[sub(1)](x[sub(1)], y[sub(1)],z[sub(1)]) and P[sub(2)](x[sub(2)], y[sub(2)], z[sub(2)]) in Parametric Form
Angle between Two Lines with Direction Cosines
General Equation of a Plane
Equation of Plane Passing through Points
Equation of Plane in Intercept Form
Equations of Line through (x[sub(0)], y[sub(0)], z[sub(0)]) and Perpendicular to Plane
Distance from Point (x, y, z) to Plane Ax + By + D= 0
Normal form for Equation of Plane
Transformation of Coordinates Involving Pure Translation
Transformation of Coordinates Involving Pure Rotation
Transformation of Coordinates Involving Translation and Rotation
Cylindrical Coordinates (r, θ, z)
Spherical Coordinates (r, θ, φ)
Logarithmic Identities
Special Values
Logarithms to General Base
Series Expansions
Limiting Values
Inequalities
Continued Fractions
Polynomial Approximations
Fundamental Properties
Definition of General Powers
Logarithmic and Exponential Functions
Polynomial Approximations
Slopes
Trigonometric Ratios
Sine Law
Cosine Law
Algebra
Expanding
Factoring
Roots of Quadratic
Law of Exponents
Logarithms
Chapter 5 Statistical Methods for Data Analytics
Introduction
Discrete Distributions
Bernoulli Distribution
Beta Binomial Distribution
Beta Pascal Distribution
Binomial Distribution
Discrete Weibull Distribution
Geometric Distribution
Hypergeometric Distribution
Negative Binomial Distribution
Poisson Distribution
Rectangular (Discrete Uniform) Distribution
Continuous Distributions
Arcsin Distribution
Beta Distribution
Cauchy Distribution
Chi Distribution
Chi-Square Distribution
Erlang Distribution
Exponential Distribution
Extreme-Value Distribution
F Distribution
Gamma Distribution
Half-Normal Distribution
Laplace (Double Exponential) Distribution
Logistic Distribution
Lognormal Distribution
Noncentral Chi-Square Distribution
Noncentral F Distribution
Noncentral t Distribution
Normal Distribution
Pareto Distribution
Rayleigh Distribution
t Distribution
Triangular Distribution
Uniform Distribution
Weibull Distribution
Distribution Parameters
Average
Variance
Standard Deviation
Standard Error
Skewness
Standardized Skewness
Kurtosis
Standardized Kurtosis
Weighted Average
Estimation and Testing
100(1 − α)% Confidence Interval for Mean
100(1 − α)% Confidence Interval for Variance
100(1 − α)% Confidence Interval for Difference in Means
Equal Variance
Unequal Variance
100(1 − α)% Confidence Interval for ratio of variances
Normal Probability Plot
Comparison of Poisson Rates
Distribution Functions and Parameter Estimation
Bernoulli
Binomial
Discrete Uniform
Geometric
Negative Binomial
Poisson
Beta
Chi-Square
Erlang
Exponential
F
Gamma
Lognormal
System Displays
Normal
Student’s t
Triangular
Uniform
Weibull
Chi-Square Test for Distribution Fitting
Kolmogorov–Smirnov Test
ANOVA (Analysis of Variance)
Notations
Standard Error (Internal)
Standard Error (Pooled)
Interval Estimates
Tukey Interval
Scheffe Interval
Cochran C-Test
Bartlett Test
Hartley’s Test
Kruskal–Wallis Test
Freidman Test
Regression
Notations
Regression Statistics
Predictions
Nonlinear Regression
Ridge Regression
Quality Control
Subgroup Statistics
X-Bar Charts
Capability Ratios
R Charts
S Charts
C Charts
U Charts
P Charts
NP Charts
CuSum Chart for the Mean
Multivariate Control Charts
Time Series Analysis
Notations
Autocorrelation at Lag k
Partial Autocorrelation at Lag k
Cross-Correlation at Lag k
Box-Cox
Periodogram (Computed Using Fast Fourier Transform)
Categorical Analysis
Notations
Totals
Chi-Square
Fisher’s Exact Test
Lambda
Uncertainty Coefficient
Somer’s D
Eta
Contingency Coefficient
Cramer’s V
Conditional Gamma
Pearson’s r
Kendall’s Tau b
Tau C
Probability Terminology
Basic Probability Principles
Random Variable
Mean Value x or Expected Value μ
Discrete Distribution Formulas
Bernoulli Distribution
Beta Binomial Distribution
Beta Pascal Distribution
Binomial Distribution
Discrete Weibull Distribution
Geometric Distribution
Hypergeometric Distribution
Negative Binomial Distribution
Poisson Distribution
Rectangular (Discrete Uniform) Distribution
Continuous Distribution Formulas
Arcsin Distribution
Beta Distribution
Cauchy Distribution
Chi Distribution
Chi-Square Distribution
Erlang Distribution
Exponential Distribution
Extreme-Value Distribution
F Distribution
Gamma Distribution
Half-Normal Distribution
Laplace (Double Exponential) Distribution
Logistic Distribution
Lognormal Distribution
Noncentral Chi-Square Distribution
Noncentral F Distribution
Noncentral t Distribution
Normal Distribution
Pareto Distribution
Rayleigh Distribution
t Distribution
Triangular Distribution
Uniform Distribution
Weibull Distribution
Variate Generation Techniques
Reference
Chapter 6 Descriptive Statistics for Data Presentation
Introduction
Sample Average
Sample Variance
Sample Standard Deviation
Sample Standard Error of the Mean
Skewness
Standardized Skewness
Kurtosis
Standardized Kurtosis
Weighted Average
Estimation and Testing
100(1 − α)% Confidence Interval for Mean
100(1 − α)% Confidence Interval for Variance
100(1 − α)% Confidence Interval for Difference in Means
For Equal Variance
For Unequal Variance
100(1 − α)% Confidence Interval for Ratio of Variances
Normal Probability Plot
Comparison of Poisson Rates
Distribution functions and Parameter Estimation
Bernoulli Distribution
Binomial Distribution
Discrete Uniform Distribution
Geometric Distribution
Negative Binomial Distribution
Poisson Distribution
Beta Distribution
Chi-Square Distribution
Erlang Distribution
Exponential Distribution
F Distribution
Gamma Distribution
Lognormal Distribution
Normal Distribution
Student’s t
Triangular Distribution
Uniform Distribution
Weibull Distribution
Chi-Square Test for Distribution Fitting
Kolmogorov–Smirnov Test
ANOVA (Analysis of Variance)
Notations
Standard Error
Interval Estimates
Tukey Interval
Scheffe Interval
Cochran C-test
Bartlett Test
Hartley’s Test
Kruskal–Wallis Test
Freidman Test
Regression
Notations
Statistical Quality Control
Subgroup Statistics
X-Bar Charts
Capability Ratios
R Charts
S Charts
C Charts
U Charts
P Charts
NP Charts
CuSum Chart for the Mean
Time Series Analysis
Notations
Autocorrelation at Lag k
Partial Autocorrelation at Lag k
Cross-Correlation at Lag k
Box-Cox Computation
Periodogram (Computed Using Fast Fourier Transform)
Categorical Analysis
Notations
Totals
Chi-Square
Lambda
Uncertainty Coefficient
Somer’s D Measure
Eta
Contingency Coefficient
Cramer’s V Measure
Conditional Gamma
Pearson’s r Measure
Kendall’s Tau b Measure
Tau C Measure
Overall Mean
Chebyshev’s Theorem
Per mutation
Combination
Failure
Chapter 7 Data Analytics Tools for Understanding Random Field Regression Models
Introduction
RFR Models
Two Examples
Bayesian Regression Models and Random Fields
Data Analysis: Finding the Associated Regression Model
Relating Eigenvectors to Regression Functions
Some Special Random Field Models
Gaussian Covariance as Damped Polynomial Regression
Trigonometric Regression and Spline Covariance
Discussion
References
Chapter 8 Application of DEJI Systems Model to Data Integration
Introduction to Data Integration
Leveraging the Input-Control-Output-Mechanism Model
Data Types and Fidelity
Data Collection and Sanitization
DEJI Systems Model for Data Quality
Data Value Model
Data Quality Control
References
Index
