STATISTICS

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 (...

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...

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 ....

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...