Data Analytics: Handbook of Formulas and Techniques

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