STATISTICS
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3 A Level in Statistics 
Population variance, σ 
2 
, = 
∑x2 
 N − μ2 = N1 ∑(x − μ)2 
Population standard deviation, σ, = 
∑N x2 − μ2 = N1 ∑(x − μ)2 
Sample variance, s 
2 
, = 
n 1− 1 2 (∑x)2 1 1 ∑(x − x)2 
∑x − n n − 
Sample standard deviation, s, = 
Binomial probability calculations: P(X 
= x) n x px (1 − p)n −x 
Binomial mean = np 
Binomial variance = np (1 − p) 
For a random sample of nx observations from N( 
μ 
, σ 
2 
) 
1 
1 
1 
1 
2 
2 
2 
...
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3 A Level in Statistics 
Population variance, σ 
2 
, = 
∑x2 
 N − μ2 = N1 ∑(x − μ)2 
Population standard deviation, σ, = 
∑N x2 − μ2 = N1 ∑(x − μ)2 
Sample variance, s 
2 
, = 
n 1− 1 2 (∑x)2 1 1 ∑(x − x)2 
∑x − n n − 
Sample standard deviation, s, = 
Binomial probability calculations: P(X 
= x) n x px (1 − p)n −x 
Binomial mean = np 
Binomial variance = np (1 − p) 
For a random sample of nx observations from N( 
μ 
, σ 
2 
) 
1 
1 
1 
1 
2 
2 
2 
...
descriptive statistics
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MCQ 16.1 
An orderly set of data arranged in accordance with their time of occurrence is called: 
(a) Arithmetic series (b) Harmonic series (c) Geometric series (d) Time series 
MCQ 16.2 
A time series consists of: 
(a) Short-term variations (b) Long-term variations (c) Irregular variations (d) All of the above 
MCQ 16.3 
The graph of time series is called: 
(a) Histogram (b) Straight line (c) Historigram (d) Ogive 
MCQ 16.4 
Secular trend can be measured by: 
(a) Two methods (b) Three methods (...
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MCQ 16.1 
An orderly set of data arranged in accordance with their time of occurrence is called: 
(a) Arithmetic series (b) Harmonic series (c) Geometric series (d) Time series 
MCQ 16.2 
A time series consists of: 
(a) Short-term variations (b) Long-term variations (c) Irregular variations (d) All of the above 
MCQ 16.3 
The graph of time series is called: 
(a) Histogram (b) Straight line (c) Historigram (d) Ogive 
MCQ 16.4 
Secular trend can be measured by: 
(a) Two methods (b) Three methods (...
Table of Contents 
Preface ......................................................................................................................ix 
Acknowledgment ................................................................................................ xiii 
About the Editors ..................................................................................................xv 
Authors’ Disclosures ......................................................................................... ...
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Table of Contents 
Preface ......................................................................................................................ix 
Acknowledgment ................................................................................................ xiii 
About the Editors ..................................................................................................xv 
Authors’ Disclosures ......................................................................................... ...
CONTENTS 
PREFACE xxi 
ACKNOWLEDGMENTS xxix 
PART I 
DATA PREPARATION 1 
CHAPTER 1 AN INTRODUCTION TO DATA MINING AND PREDICTIVE 
ANALYTICS 3 
1.1 What is Data Mining? What is Predictive Analytics? 3 
1.2 Wanted: Data Miners 5 
1.3 The Need for Human Direction of Data Mining 6 
1.4 The Cross-Industry Standard Process for Data Mining: CRISP-DM 6 
1.4.1 CRISP-DM: The Six Phases 7 
1.5 Fallacies of Data Mining 9 
1.6 What Tasks Can Data Mining Accomplish 10 
1.6.1 Description 10 
1.6.2 Estimation 1...
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CONTENTS 
PREFACE xxi 
ACKNOWLEDGMENTS xxix 
PART I 
DATA PREPARATION 1 
CHAPTER 1 AN INTRODUCTION TO DATA MINING AND PREDICTIVE 
ANALYTICS 3 
1.1 What is Data Mining? What is Predictive Analytics? 3 
1.2 Wanted: Data Miners 5 
1.3 The Need for Human Direction of Data Mining 6 
1.4 The Cross-Industry Standard Process for Data Mining: CRISP-DM 6 
1.4.1 CRISP-DM: The Six Phases 7 
1.5 Fallacies of Data Mining 9 
1.6 What Tasks Can Data Mining Accomplish 10 
1.6.1 Description 10 
1.6.2 Estimation 1...
Preface xix 
About the Companion Website xxxiii 
1 Preliminary Considerations 1 
1.1 
The Philosophical Bases of Knowledge: Rationalistic versus 
Empiricist Pursuits, 1 
1.2 
What is a “Model”?, 4 
1.3 
Social Sciences versus Hard Sciences, 6 
1.4 
Is Complexity a Good Depiction of Reality? Are Multivariate 
Methods Useful?, 8 
1.5 
Causality, 9 
1.6 
The Nature of Mathematics: Mathematics as a Representation 
of Concepts, 10 
1.7 
As a Social Scientist, How Much Mathematics Do You Need 
to ...
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Preface xix 
About the Companion Website xxxiii 
1 Preliminary Considerations 1 
1.1 
The Philosophical Bases of Knowledge: Rationalistic versus 
Empiricist Pursuits, 1 
1.2 
What is a “Model”?, 4 
1.3 
Social Sciences versus Hard Sciences, 6 
1.4 
Is Complexity a Good Depiction of Reality? Are Multivariate 
Methods Useful?, 8 
1.5 
Causality, 9 
1.6 
The Nature of Mathematics: Mathematics as a Representation 
of Concepts, 10 
1.7 
As a Social Scientist, How Much Mathematics Do You Need 
to ...
Contents 
2.4 BasicMatrixOperations . . . . . . . . . . . . . . . . . . . . . . . . . . 25 
a. Equality, Addition, and Multiplication of Matrices . . . . . . . . . . . 26 
b. Matrix Transposition . . . . . . . . . . . . . . . . . . . . . . . . . . 28 
c. Some Special Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 29 
d. Trace and the Euclidean Matrix Norm . . . . . . . . . . . . . . . . . 30 
e. Kronecker and Hadamard Products . . . . . . . . . . . . . . . . . . . 32 
f. DirectSums ....
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Contents 
2.4 BasicMatrixOperations . . . . . . . . . . . . . . . . . . . . . . . . . . 25 
a. Equality, Addition, and Multiplication of Matrices . . . . . . . . . . . 26 
b. Matrix Transposition . . . . . . . . . . . . . . . . . . . . . . . . . . 28 
c. Some Special Matrices . . . . . . . . . . . . . . . . . . . . . . . . . 29 
d. Trace and the Euclidean Matrix Norm . . . . . . . . . . . . . . . . . 30 
e. Kronecker and Hadamard Products . . . . . . . . . . . . . . . . . . . 32 
f. DirectSums ....
Contents 
1 First steps in the analysis of functional data 1 
1.1 Basis expansions . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Sample mean and covariance . . . . . . . . . . . . . . . . . . 6 
1.3 Principal component functions . . . . . . . . . . . . . . . . . 10 
1.4 Analysis of BOA stock returns . . . . . . . . . . . . . . . . . 11 
1.5 Diusion tensor imaging . . . . . . . . . . . . . . . . . . . . 14 
1.6 Chapter 1 problems . . . . . . . . . . . . . . . . . . . . . . . 17 
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Contents 
1 First steps in the analysis of functional data 1 
1.1 Basis expansions . . . . . . . . . . . . . . . . . . . . . . . . . 3 
1.2 Sample mean and covariance . . . . . . . . . . . . . . . . . . 6 
1.3 Principal component functions . . . . . . . . . . . . . . . . . 10 
1.4 Analysis of BOA stock returns . . . . . . . . . . . . . . . . . 11 
1.5 Diusion tensor imaging . . . . . . . . . . . . . . . . . . . . 14 
1.6 Chapter 1 problems . . . . . . . . . . . . . . . . . . . . . . . 17 
2 Fur...
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