Business Analytics and Statistics

677 Pages·2018·25.027 MB·English

by  Ken Black, Nelson Perera, John Asafu-Adjaye, Paul Burke, Carl Sherwood, Saleh Wasimi

BUSINESS ANALYTICS
AND STATISTICS
BLACK | ASAFU-ADJAYE | BURKE | KHAN | KING
PERERA | PAPADIMOS | SHERWOOD | WASIMI

Business analytics
and statistics
FIRST EDITION
Ken Black
John Asafu-Adjaye
Paul Burke
Nazim Khan
Gerard King
Nelson Perera
Andrew Papadimos
Carl Sherwood
Saleh Wasimi
Firsteditionpublished2019by
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10 9 8 7 6 5 4 3 2 1
BRIEF CONTENTS
Preface ix
Keyfeatures x
Abouttheauthors xi
1.Dataandbusinessanalytics 1
2.Datavisualisation 17
3.Descriptivesummarymeasures 60
4.Probability 108
5.Discretedistributions 155
6.Thenormaldistributionandothercontinuousdistributions 191
7.Samplingandsamplingdistributions 215
8.Statisticalinference:estimationforsinglepopulations 249
9.Statisticalinference:hypothesistestingforsinglepopulations 285
10.Statisticalinferencesabouttwopopulations 335
11.Analysisofvarianceanddesignofexperiments 397
12.Chi-squaretests 444
13.Simpleregressionanalysis 471
14.Multipleregressionanalysis 518
15.Time-seriesforecastingandindexnumbers 553
AppendixA:Tables 619
AppendixB:Fundamentalsymbolsandabbreviations 656
Index 659
CONTENTS
Preface ix CHAPTER 3
Keyfeatures x
Descriptive summary
Abouttheauthors xi
measures 60
CHAPTER 1
Introduction 61
Data and business analytics 1
3.1Measuresofcentraltendency 62
Introduction 2 Mode 62
1.1Informingbusinessstrategy 2 Median 63
1.2Businessanalytics 3 Mean 64
1.3Basicstatisticalconcepts 4 3.2Measuresoflocation 67
Typesofdata 6 Percentiles 67
1.4Bigdata 7 Quartiles 69
1.5Datamining 9 3.3Measuresofvariability 71
Machinelearning 11 Range 72
Summary 13 Interquartilerange 72
Keyterms 14 Varianceandstandarddeviation 73
Reviewproblems 14 Populationversussamplevarianceandstandard
References 16 deviation 79
Acknowledgements 16 Computationalformulasforvarianceandstandard
deviation 81
z-scores 83
CHAPTER 2
Coefficientofvariation 84
Data visualisation 17
3.4Measuresofshape 86
Introduction 18 Skewness 87
2.1Frequencydistributions 18 Skewnessandtherelationshipofthemean,median
Classmidpoint 20 andmode 88
Relativefrequency 20 Coefficientofskewness 88
Cumulativefrequency 20 Kurtosis 88
2.2Basicgraphicaldisplaysofdata 24 Box-and-whiskerplots 89
Histograms 24 3.5Measuresofassociation 93
Frequencypolygons 28 Correlation 93
Ogives 30 Summary 100
Piecharts 32 Keyterms 101
Stem-and-leafplots 33 Keyequations 102
Paretocharts 35 Reviewproblems 103
Scatterplots 37 Mathsappendix 106
2.3Multidimensionalvisualisation 41 Acknowledgements 107
Representations 42
Manipulations 48 CHAPTER 4
2.4Datavisualisationtools 51 Probability 108
Interactivevisualisations 51
Visualisationsoftware 53 Introduction 109
Summary 54 4.1Methodsofdeterminingprobabilities 110
Keyterms 54 Classicalmethod 110
Reviewproblems 55 Relativefrequencyofoccurrencemethod 111
Acknowledgements 59 Subjectiveprobabilitymethod 112
4.2Structureofprobability 114 GraphingPoissondistributions 181
Experiment 114 Poissonapproximationofthebinomial
Event 114 distribution 182
Elementaryevents 114 Summary 187
Samplespace 114 Keyterms 187
Setnotation,unionsandintersections 115 Keyequations 188
Mutuallyexclusiveevents 116 Reviewproblems 188
Independentevents 117 Acknowledgements 190
Collectivelyexhaustiveevents 118
Complementaryevents 118 CHAPTER 6
4.3Contingencytablesandprobability The normal distribution
matrices 120
and other continuous
Marginal,union,jointandconditional
probabilities 120 distributions 191
Probabilitymatrices 121
Introduction 192
4.4Additionlaws 124
6.1Thenormaldistribution 192
Generallawofaddition 124
Historyandcharacteristicsofthenormal
Speciallawofaddition 129
distribution 194
4.5Multiplicationlaws 132
6.2Thestandardisednormaldistribution 196
Generallawofmultiplication 132
6.3Solvingnormaldistributionproblems 198
Speciallawofmultiplication 133
6.4Thenormaldistributionapproximation
4.6Conditionalprobability 136
tothebinomialdistribution 202
Assessingindependence 139
6.5Theuniformdistribution 205
Treediagrams 141
6.6Theexponentialdistribution 209
RevisingprobabilitiesandBayes’rule 143
Probabilitiesfortheexponentialdistribution 210
Summary 148
Summary 212
Keyterms 149
Keyterms 212
Keyequations 149
Keyequations 212
Reviewproblems 150
Reviewproblems 213
Acknowledgements 154
Acknowledgements 214
CHAPTER 5
CHAPTER 7
Discrete distributions 155
Sampling and sampling
Introduction 156 distributions 215
5.1Discreteversuscontinuousdistributions 156
Introduction 216
5.2Describingadiscretedistribution 158
7.1Sampling 216
Mean,varianceandstandarddeviationofdiscrete
Reasonsforsampling 216
distributions 159
Reasonsfortakingacensus 217
5.3Binomialdistribution 163
Samplingframe 218
Assumptionsaboutthebinomialdistribution 163
7.2Randomversusnonrandomsampling 218
Solvingabinomialproblem 165
Randomsamplingtechniques 219
Usingthebinomialtable 169
Nonrandomsampling 223
Meanandstandarddeviationofabinomial
7.3Typesoferrorsfromcollecting
distribution 171
sampledata 225
Graphingbinomialdistributions 172
Samplingerror 225
5.4Poissondistribution 176
Nonsamplingerrors 226
SolvingPoissonproblemsbyformula 178
7.4Samplingdistributionofthesample
MeanandstandarddeviationofaPoisson
mean,x̄ 227
distribution 180
CONTENTS v
Centrallimittheorem 231 9.2Thesix-stepapproachtohypothesis
Samplingfromafinitepopulation 236 testing 296
7.5Samplingdistributionofthesample Step1:SetupH andH 296
0 a
proportion,p̂ 239 Step2:Decideonthetypeanddirection
Summary 244 ofthetest 296
Keyterms 245 Step3:Decideonthelevelofsignificance(𝛼),
Keyequations 246 determinethecriticalvalue(s)andregion(s),and
Reviewproblems 246 drawadiagram 296
Acknowledgements 248 Step4:Writedownthedecisionrule 296
Step5:Selectarandomsampleanddorelevant
CHAPTER 8 calculations 296
Statistical inference: estimation Step6:Drawaconclusion 297
9.3Hypothesistestsforapopulationmean:large
for single populations 249
samplecase(zstatistic,𝜎known) 297
Introduction 250 Step1:SetupH0andHa 298
8.1Estimatingthepopulationmeanusingthe Step2:Decideonthetypeanddirection
zstatistic(𝜎known) 250 ofthetest 298
Finitepopulationcorrectionfactor 256 Step3:Decideonthelevelofsignificance(𝛼),
Estimatingthepopulationmeanusingthezstatistic determinethecriticalvalue(s)andregion(s),and
whenthesamplesizeissmall 257 drawadiagram 298
8.2Estimatingthepopulationmeanusingthe Step4:Writedownthedecisionrule 299
tstatistic(𝜎unknown) 259 Step5:Selectarandomsampleanddorelevant
Thetdistribution 260 calculations 299
Robustness 260 Step6:Drawaconclusion 299
Characteristicsofthetdistribution 260 Testingthemeanwithafinitepopulation 300
Readingthetdistributiontable 261 Thecriticalvaluemethod 300
Confidenceintervalstoestimatethepopulation Thep-valuemethod 302
meanusingthetstatistic 262 9.4Hypothesistestsaboutapopulationmean:
8.3Estimatingthepopulationproportion 266 smallsamplecase(tstatistic,𝜎unknown) 306
8.4Estimatingthepopulationvariance 270 9.5Testinghypothesesaboutaproportion 311
8.5Estimatingsamplesize 274 9.6Testinghypothesesaboutavariance 316
Samplesizewhenestimating𝜇 274 9.7SolvingforTypeIIerrors 320
Determiningsamplesizewhenestimatingp 276 SomeobservationsaboutTypeIIerrors 325
Summary 280 Operatingcharacteristicandpowercurves 325
Keyterms 281 Effectofincreasingsamplesizeontherejection
Keyequations 281 limits 326
Reviewproblems 282 Summary 330
Acknowledgements 284 Keyterms 331
Keyequations 332
CHAPTER 9 Reviewproblems 332
Acknowledgements 334
Statistical inference: hypothesis
testing for single CHAPTER 10
populations 285 Statistical inferences about two
populations 335
Introduction 286
9.1Hypothesis-testingfundamentals 286 Introduction 336
Rejectionandnonrejectionregions 289 10.1Hypothesistestingandconfidenceintervalsfor
TypeIandTypeIIerrors 292 thedifferencebetweentwomeans(zstatistic,
Howarealphaandbetarelated? 294 populationvariancesknown) 336
vi CONTENTS
Hypothesistesting 337 Reviewproblems 436
Confidenceintervals 343 Mathsappendix 441
10.2Hypothesistestingandconfidenceintervalsfor Acknowledgements 443
thedifferencebetweentwomeans(tstatistic,
populationvariancesunknown) 349 CHAPTER 12
Hypothesistesting 350 Chi-square tests 444
Confidenceintervals 357
Introduction 445
10.3Statisticalinferencesabouttwopopulations
12.1Chi-squaregoodness-of-fittest 445
withpairedobservations 362
Step1:SetupH andH 447
Hypothesistesting 363 0 a
Step2:Decideonthetypeoftest 447
Confidenceintervals 368
Step3:Decideonthelevelofsignificance𝜶and
10.4Statisticalinferencesabouttwopopulation
determinethecriticalvalue(s)andregion(s) 448
proportions 373
Step4:Writedownthedecisionrule 448
Hypothesistesting 374
Step5:Selectarandomsampleanddorelevant
Confidenceintervals 378
calculations 448
10.5Statisticalinferencesabouttwopopulation
Step6:Drawaconclusion 448
variances 381
12.2Contingencyanalysis:chi-squaretestof
Hypothesistesting 382
independence 458
Confidenceintervals 387
Step1:SetupH andH 460
Summary 390 0 a
Step2:Decideonthetypeoftest 460
Keyterms 390
Step3:Decideonthelevelofsignificance𝜶and
Keyequations 391
determinethecriticalvalue(s)andregion(s) 460
Reviewproblems 392
Step4:Writedownthedecisionrule 460
Mathsappendix 396
Step5:Selectarandomsampleanddorelevant
Acknowledgements 396
calculations 460
Step6:Drawaconclusion 461
CHAPTER 11
Summary 466
Analysis of variance and design
Keyterms 466
of experiments 397 Keyequations 466
Reviewproblems 467
Introduction 398
Acknowledgements 470
11.1Introductiontodesignofexperiments 398
11.2Thecompletelyrandomiseddesign
CHAPTER 13
(one-wayANOVA) 400
ReadingtheFdistributiontable 404 Simple regression analysis 471
11.3Multiplecomparisontests 409
Introduction 472
Tukey’shonestlysignificantdifference(HSD)test:
13.1Examiningtherelationshipbetweentwo
Thecaseofequalsamplesizes 409
variables 472
Tukey–Kramerprocedure:Thecaseofunequal
13.2Determiningtheequationofthe
samplesizes 413
regressionline 475
11.4Therandomisedblockdesign 415
13.3Residualanalysis 485
11.5Afactorialdesign(two-wayANOVA) 421
Usingresidualstotesttheassumptionsofthe
Advantagesoffactorialdesign 422
regressionmodel 488
Factorialdesignswithtwotreatments 422
13.4Standarderroroftheestimate 492
Statisticallytestingafactorialdesign 423
13.5Coefficientofdetermination 497
Interaction 424
Relationshipbetweenrandr2 499
Summary 434
13.6Hypothesistestsfortheslopeoftheregression
Keyterms 435
modelandtestingtheoverallmodel 500
Keyequations 436
Testingtheslope 500
CONTENTS vii
13.7Estimationandprediction 505 CHAPTER 15
Confidence(prediction)intervalstoestimatethe
Time-series forecasting and
conditionalmeanofy:𝜇 505
y/x
index numbers 553
Predictionintervalstoestimateasingle
valueofy 506 Introduction 554
Interpretingtheoutput 510 15.1Componentsofatimeseries 554
Summary 511 Trendcomponent 554
Keyterms 512 Seasonalcomponent 554
Keyequations 512 Cyclicalcomponent 555
Reviewproblems 513 Irregular(orrandom)component 555
Acknowledgements 517 15.2Time-seriessmoothingmethods 557
Themovingaveragemethod 557
CHAPTER 14 Theexponentialsmoothingmethod 561
Multiple regression Seasonalindices 563
Deseasonalisingtimeseries 567
analysis 518
15.3Leastsquarestrend-basedforecasting
Introduction 519 models 573
14.1Themultipleregressionmodel 519 Thelineartrendmodel 573
Multipleregressionmodelwithtwoindependent Thequadratictrendmodel 577
variables(first-order) 521 Theexponentialtrendmodel 578
Determiningthemultipleregressionequation 521 15.4Autoregressivetrend-basedforecasting
14.2Significancetestsoftheregressionmodeland models 582
itscoefficients 528 Testingforautocorrelation 582
Testingtheoverallmodel 528 Waystoovercometheautocorrelation
Significancetestsoftheregression problem 585
coefficients 530 15.5Evaluatingalternativeforecastingmodels 593
14.3Residuals,standarderroroftheestimate 15.6Indexnumbers 597
andR2 534 Simplepriceindex 597
Residuals 534 Aggregatepriceindices 597
SSEandstandarderroroftheestimate 536 Changingthebaseperiod 603
Coefficientofmultipledetermination(R2) 539 Applicationsofpriceindices 605
AdjustedR2 540 Summary 608
14.4Interpretingmultipleregressioncomputer Keyterms 609
output 543 Keyequations 610
Are-examinationofmultipleregression Reviewproblems 611
output 543 Acknowledgements 618
Summary 546
Keyterms 546 AppendixA:Tables 619
Keyequations 547 AppendixB:Fundamentalsymbolsand
Reviewproblems 547 abbreviations 656
Acknowledgements 552 Index 659
viii CONTENTS