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Samenvatting Statistiek Voor Bedrijfswetenschappen (Y50234)

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Statistiek Voor Bedrijfswetenschappen (Y50234)

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Katholieke Universiteit Leuven (KU Leuven)

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Uploaded on February 9, 2022
Number of pages 261
Written in 2021/2022
Type Summary

statistiek
aj2021 2022
rfc
rstudio
patrick wessa
handelswetenschappen
statistiek voor bedrijfswetenschappen
kul
schakeljaar handelswetenschappen

Institution
Katholieke Universiteit Leuven (KU Leuven)
Education
Schakeljaar Handelswetenschappen
Course
Statistiek Voor Bedrijfswetenschappen (Y50234)

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Statistiek voor
bedrijfswetenschappen
Notities

Docent: Patrick Wessa
Academiejaar: 2021 - 2022

,
,INHOUDSOPGAVE
HOOFDSTUK 1: Getting Started ...................................................................................................... 1
1.1.2.0.6 Compendium.................................................................................................................. 1
1.4.1 Werking R Framework ......................................................................................................... 1
1.4.2 Univariaat ............................................................................................................................ 1
1.4.3 Bivariaat............................................................................................................................... 1
1.4.4 Trivariaat .............................................................................................................................. 1
1.4.5 Multivariaat .......................................................................................................................... 1
1.4.7 Reproduceren ...................................................................................................................... 1
1.5 Collaborative Compendium Writing ......................................................................................... 1
1.7 Instant Messaging ................................................................................................................... 2
HOOFDSTUK 2: Introduction to Probability...................................................................................... 3
2.1 Definities van waarschijnlijkheden........................................................................................... 3
2.1.0.0.2 Doorsnede ..................................................................................................................... 3
2.1.0.0.3 Unie ............................................................................................................................... 3
2.1.0.0.6 Exclusiveness ................................................................................................................ 3
2.3. Theorema van Bayes ............................................................................................................. 4
2.3.0.0.2 Voorbeeld ...................................................................................................................... 6
2.3.0.0.3 Sensitiviteit en Specificiteit ............................................................................................. 7
2.4 Multinomiale Naive Bayes Classificatiemodel ......................................................................... 9
2.4.2 Voorbeeld ............................................................................................................................ 9
2.4.3 Interactie-effecten .............................................................................................................. 10
2.4.4 Nulkansen .......................................................................................................................... 11
2.4.5 Types of Naive Bayes Classifiers ....................................................................................... 12
2.5 Wet van de grote getallen ..................................................................................................... 12
2.5.1 Weak Law of Large Numbers ............................................................................................. 16
HOOFDSTUK 3: Probability Distributions ...................................................................................... 19
3.1. Statistische maatregelen van de waarschijnlijkheidsverdeling .............................................. 19
3.2 Discrete verdelingen ............................................................................................................. 19
3.2.1 Bernoulli verdeling ............................................................................................................. 19
3.2.1.6 Doel ................................................................................................................................ 19
3.2.2 Binomiale verdeling............................................................................................................ 20

,3.2.2.6 R Module ........................................................................................................................ 20
3.2.2.7 Voorbeeld ....................................................................................................................... 22
3.2.3 Multinomiale verdeling ....................................................................................................... 22
3.2.3.4. Doel ............................................................................................................................... 22
3.3 Continue verdelingen ............................................................................................................ 22
3.3.1 Uniforme verdeling ............................................................................................................. 22
3.3.1.1 Dichtheidsfunctie............................................................................................................. 23
3.3.1.2 Verdelingsfunctie ............................................................................................................ 23
3.3.1.11 Doel .............................................................................................................................. 23
3.3.1.12 Voorbeeld ..................................................................................................................... 23
3.3.2 Normaalverdeling (of Gauss curve) .................................................................................... 24
3.3.2.1 Dichtheidsfunctie............................................................................................................. 24
3.3.2.2 Verdelingsfunctie ............................................................................................................ 24
3.3.2.19 Parameter Estimation.................................................................................................... 25
3.3.2.19.1 R Module ................................................................................................................... 25
3.3.2.19.2 Voorbeeld .................................................................................................................. 26
3.3.2.20 Random number generator ........................................................................................... 27
3.3.2.20.1 R Module ................................................................................................................... 28
3.3.2.20.2 Voorbeeld .................................................................................................................. 30
3.3.2.34 Doel .............................................................................................................................. 30
3.3.2.35 Gaussian (of : Normal) Naive Bayes Classifier .............................................................. 30
3.3.2.35.2 R Module ................................................................................................................... 30
3.3.2.35.3 Voorbeeld .................................................................................................................. 34
3.3.3 Chi verdeling ...................................................................................................................... 34
3.3.3.4 Random number generator ............................................................................................. 34
3.3.4 Chi-kwadraatverdeling (met 1 parameter) .......................................................................... 34
3.3.4.11 R Module ...................................................................................................................... 35
3.3.4.12 Voorbeeld ..................................................................................................................... 35
3.3.4.13 Random number generator ........................................................................................... 36
3.3.4.16 Relaties met andere functies ......................................................................................... 36
3.3.6 Student T verdeling ............................................................................................................ 37
3.3.6.9 Random number generator ............................................................................................. 37
3.3.7 Fisher F verdeling .............................................................................................................. 38

, 3.3.7.9 Random generator .......................................................................................................... 38
Conclusies .................................................................................................................................. 38
HOOFDSTUK 4: Descriptieve statistiek en exploratieve data analyses.......................................... 41
4.1 Types of data ........................................................................................................................ 41
4.1.1 Kwalitatieve data ................................................................................................................ 41
4.1.2 Kwantitatieve data.............................................................................................................. 41
4.2 Kwalitatieve data................................................................................................................... 42
4.2.2 Frequency Plot................................................................................................................... 42
4.2.2.2 R Module ........................................................................................................................ 42
4.2.2.3 Doel ................................................................................................................................ 43
4.2.3 Frequentietabel .................................................................................................................. 43
4.2.3.2 R Module ........................................................................................................................ 43
4.2.4 Contingentietabel ............................................................................................................... 43
4.2.4.2 Voorbeeld ....................................................................................................................... 44
4.2.5 Binomiale classificatie maatstaven. .................................................................................... 44
4.2.5.2 Voorbeeld ....................................................................................................................... 44
4.2.5.3 Confusion Matrix ............................................................................................................. 45
4.3 Kwantitatieve data ................................................................................................................ 46
4.3.1 Stem-and-Leaf Plot (NL: stam en blad) .............................................................................. 46
4.3.1.2 R Module ........................................................................................................................ 46
4.3.1.4.1 Voordeel ...................................................................................................................... 46
4.3.1.5 Voorbeeld ....................................................................................................................... 47
4.3.2 Histogram .......................................................................................................................... 47
4.3.2.2 R Module ........................................................................................................................ 47
4.3.2.3 Doel ................................................................................................................................ 49
4.3.2.4.2 Nadeel ......................................................................................................................... 49
4.3.2.5 Voorbeeld ....................................................................................................................... 49
4.3.3 Kwantielen ......................................................................................................................... 50
4.3.3.1 Kwantielen gebaseerd op gewogen gemiddelden op Xnq ................................................ 50
4.3.3.1.2 Voorbeeld .................................................................................................................... 50
4.3.3.9 Harrel-Davis kwantielen .................................................................................................. 52
4.3.4 Central Tendency............................................................................................................... 53
4.3.4.2 Rekenkundig gemiddelde ................................................................................................ 53

,4.3.4.2.9 Nadelen ....................................................................................................................... 53
4.3.4.3 Gewogen gemiddelde ..................................................................................................... 53
4.3.4.4 Geometrisch gemiddelde ................................................................................................ 53
4.3.4.4.2 Doel ............................................................................................................................. 53
4.3.4.4.4 Voorbeeld .................................................................................................................... 53
4.3.4.5 Harmonisch gemiddelde ................................................................................................. 54
4.3.4.5.4 Voorbeeld .................................................................................................................... 54
4.3.4.5.6 Nadelen ....................................................................................................................... 55
4.3.4.6 Kwadratisch gemiddelde ................................................................................................. 55
4.3.4.7 Root Mean Square .......................................................................................................... 55
4.3.4.12 Mediaan ........................................................................................................................ 55
4.3.4.12.2 Doel ........................................................................................................................... 55
4.3.4.12.3 Voorbeeld .................................................................................................................. 56
4.3.4.13 Midrange of Midextreme ............................................................................................... 56
4.3.4.13.3 Voorbeeld .................................................................................................................. 56
4.3.4.15 Tukey’s Trimean ........................................................................................................... 56
4.3.4.17 Trimmed Mean .............................................................................................................. 57
4.3.4.20 Doel van de Central Tendency ...................................................................................... 58
4.3.5 Variabiliteit ......................................................................................................................... 58
4.3.5.1 Range ............................................................................................................................. 58
4.3.5.4 Variantie (biased) ............................................................................................................ 58
4.3.5.5 Variantie (unbiased) ........................................................................................................ 59
4.3.5.6 Standaarddeviatie (biased) ............................................................................................. 59
4.3.5.12 Mean Absolute Deviation (MAD) ................................................................................... 59
4.3.5.17 Interkwartiel verschil...................................................................................................... 59
4.3.5.31 R Module ...................................................................................................................... 59
4.3.6.6 D’Agostino Skewness Test ............................................................................................. 60
4.3.6.8 Definition of Kurtosis ....................................................................................................... 60
4.3.6.12 Simultaan Skewness & Kurtosis testen ......................................................................... 60
4.3.6.14 R Module ...................................................................................................................... 61
4.3.8 Notched Boxplot ................................................................................................................ 63
4.3.8.16 Voordelen ..................................................................................................................... 65
4.3.8.17 Voorbeeld ..................................................................................................................... 65

,4.3.9 Scatterplot ......................................................................................................................... 66
4.3.9.2 R Module ........................................................................................................................ 66
4.3.9.5 Voorbeeld ....................................................................................................................... 68
4.3.10 Pearson Correlatie ........................................................................................................... 68
4.3.10.3 Determinatiecoëfficiënt.................................................................................................. 68
4.3.10.5 R Module ...................................................................................................................... 69
4.3.10.7 Phi coëfficiënt ............................................................................................................... 70
4.3.10.8.2 Nadelen ..................................................................................................................... 71
4.3.10.10 Taak............................................................................................................................ 71
4.3.11 Rank Correlation .............................................................................................................. 72
4.3.11.1 Spearman Rank Order Correlatie .................................................................................. 72
4.3.11.2 Kendall ’s Rank Order Correlatie ................................................................................... 72
4.3.11.3 R Module ...................................................................................................................... 72
4.3.11.5.1 Voordelen .................................................................................................................. 73
4.3.11.6 Voorbeeld 1 .................................................................................................................. 73
4.3.11.7 Voorbeeld 2 .................................................................................................................. 73
4.3.12 Partiële Pearson Correlation ............................................................................................ 74
4.3.12.2 R Module ...................................................................................................................... 74
4.3.12.5 Voorbeeld ..................................................................................................................... 75
4.3.13 Enkelvoudige Lineaire regressie ...................................................................................... 76
4.3.13.1.1 Model Assumptie 1 ................................................................................................ 76
4.3.13.1.2 Model assumptie 2 ..................................................................................................... 77
4.3.13.1.2 Model assumptie 3 ................................................................................................ 77
4.3.13.2 R Module ...................................................................................................................... 77
4.3.15 Kwantiel-Kwantiel Plot (QQ Plot) ...................................................................................... 78
4.3.15.2 R Module ...................................................................................................................... 79
4.3.15.3 Doel .............................................................................................................................. 80
4.3.17 Probability Plot Correlation Coefficient Plot (PPCC Plot) .................................................. 80
4.3.17.2 R Module ...................................................................................................................... 81
4.3.17.5 Voorbeeld ..................................................................................................................... 83
4.3.18 Kernel Density Estimation ................................................................................................ 83
4.3.18.5 Gaussian Kernel ........................................................................................................... 84
4.3.18.7 R Module ...................................................................................................................... 84

, 4.3.18.10 Voorbeeld ................................................................................................................... 85
4.3.19 Bivariate Kernel Density Plot ............................................................................................ 85
4.3.19.2 R Module ...................................................................................................................... 85
4.3.19.5 Voorbeeld ..................................................................................................................... 86
4.3.20 Bootstrap Plot (voor Central Tendency) ........................................................................... 87
4.3.20.2 R Module ...................................................................................................................... 87
4.3.20.5 Voorbeeld ..................................................................................................................... 91
4.3.21.5 Voorbeeld ..................................................................................................................... 91
4.3.22 Cronbach Alpha ............................................................................................................... 92
4.3.22.2 R Module ...................................................................................................................... 93
4.3.22.5 Voorbeeld ..................................................................................................................... 93
4.4 Kwantitatieve data met tijdsdimensie (tijdreeksen) ................................................................ 94
4.4.1 Equi-distante tijdreeksen .................................................................................................... 94
4.4.2 Tijdreeks Plot ..................................................................................................................... 94
4.4.2.2 R Module ........................................................................................................................ 95
4.4.3. Mean Plot ......................................................................................................................... 95
4.4.3.2. R Module ....................................................................................................................... 96
4.4.4 Blocked Bootstrap Plot (Central Tendency)........................................................................ 99
4.4.4.2 R Module ........................................................................................................................ 99
4.4.4.5 Voorbeeld ....................................................................................................................... 99
4.4.5 Standard Deviation-Mean Plot ........................................................................................... 99
4.4.5.5 Voorbeeld ..................................................................................................................... 100
4.4.6 Variantie reductie matrix .................................................................................................. 101
4.4.6.5 Voorbeeld ..................................................................................................................... 101
4.4.7 Partiële autocorrelatie functie ........................................................................................... 103
4.4.7.5 Voorbeeld ..................................................................................................................... 103
4.4.8 Periodogram .................................................................................................................... 106
4.4.8.5 Voorbeeld ..................................................................................................................... 107
HOOFDSTUK 5: HYPOTHESIS TESTING .................................................................................. 109
5.1.2.1 Grafiek van de normaalverdeling .................................................................................. 109
5.1.2.2 Interpretatie van standaarddeviatie ............................................................................... 109
5.2 Populatie............................................................................................................................. 110
5.9 Statistische test voor een populatiegemiddelde met een gekende variantie ........................ 110

,R Module .................................................................................................................................. 118
5.17 Toetsen van Hypothese voor onderzoek ........................................................................... 120
5.17.1 One Sample t-Test ......................................................................................................... 120
5.17.1.2 Analyse gebaseerd op kritieke waarden ...................................................................... 120
5.17.1.3 Analyse gebaseerd op p-waarden ............................................................................... 123
5.17.1.5 Alternatieven ............................................................................................................... 124
5.17.2 Skewness & Kurtosis tests ............................................................................................. 125
5.17.2.1.1 D’Agostino skewness test ........................................................................................ 125
5.17.5.1.2 Kurtosis test ............................................................................................................. 125
5.17.2.4 Alternatieven ............................................................................................................... 127
5.17.3 Gepaarde Two Sample t-Test ........................................................................................ 127
5.17.5 Unpaired Two Sample t-Test.......................................................................................... 129
5.17.5.1 Hypotheses - examples............................................................................................... 129
5.17.5.2 Analyse gebaseerd op p-waarden ............................................................................... 130
5.17.5.3 Assumpties ................................................................................................................. 132
5.17.5.4 Alternatieven ............................................................................................................... 132
15.7.6 Unpaired Two Sample Welch Test ................................................................................. 133
15.7.6.2 Analyse op basis van p-waarden ................................................................................ 133
5.17.7 Mann-Whitney U test ..................................................................................................... 133
5.17.7.1 Classical model ........................................................................................................... 134
5.17.7.1.2 Randomization model .............................................................................................. 134
5.17.7.2 Analyse op basis van p-waarden ................................................................................ 134
5.17.8 Bayesian Two Sample Test ........................................................................................... 135
5.17.9 Mediaan Test op basis van Notched Boxplots ................................................................ 135
5.17.10 Chi-kwadraat test for Count Data ................................................................................. 135
5.17.10.1 Pearson Chi-Kwadraat Test ...................................................................................... 135
5.17.10.1.4 Analyse gebaseerd op p-waarden – Output ........................................................... 136
5.17.10.1.5 Assumptie .............................................................................................................. 137
5.17.10.2 Exacte Pearson Chi-kwadraat Test met simulatie. .................................................... 137
5.17.11 One way analysis of Variance (1-way ANOVA) ............................................................ 138
5.17.11.2 Analyse gebaseerd op p-waarden ............................................................................. 138
5.17.12 Two Way Analysis of Variance (2-way ANOVA) ........................................................... 142
5.17.12.1 Analyse gebaseerd op p-waarden ............................................................................. 142

, 5.17.13 Testing Correlations ..................................................................................................... 147
5.17.14 Nota bij causaliteit ........................................................................................................ 147
HOOFDSTUK 6: Regressie modellen .......................................................................................... 149
6.1 Enkelvoudige lineair regressie model (Simple Lineair Regression Model: SLRM) ............... 149
6.1.2 Kleinste kwadratencriterium (Least Squares Criterion) ..................................................... 149
6.1.3 Ordinary Least Squares for Simple Linear Regression ..................................................... 150
6.1.4 Assumpties om regressiemodel op te stellen ................................................................... 151
6.1.5 Statistische eigenschappen van 𝛼 en 𝛽 ........................................................................... 151
6.1.5.2 Betrouwbaarheidsintervallen van eenvoudige lineaire regressieparameters ................. 153
6.2 Meervoudig lineair regressiemodel (Multiple Linear Regression Model: MLRM) ................. 154
6.2.1.3 Unbiasedness of b ........................................................................................................ 157
6.2.1.4 Minimum variantie (Gauss-Markov Theorema) ............................................................. 157
6.2.1.7 Determinatie coëfficiënt R² ............................................................................................ 158
6.2.1.8 Relatie tussen het SLRM en het MLRM ........................................................................ 158
6.2.2 Maximum Likelihood Estimation for Multiple Linear Regression ....................................... 159
Zelf regressiemodel maken met behulp van Excel en RFC ....................................................... 169
RFC: Multiple Regression (volledig uitgelegd) .......................................................................... 175
HOOFDSTUK 7: Introductie tot tijdreeksanalyse .......................................................................... 193
7.2 Case: the Market of Health and Personal Care Products .................................................... 193
7.3. Decompositie van tijdsreeksen .......................................................................................... 193
7.3.1. Klassieke decompositie van tijdsreeksen met “moving averages” ................................... 193
7.3.2 Seizoenale decompositie volgens Loess.......................................................................... 196
7.3.3. Decompositie volgens structurele tijdreeksmodellen. ...................................................... 197
7.4 Ad hoc forecasting van tijdreeksen ..................................................................................... 199
7.4.1 Regressieanalyse van tijdreeksen.................................................................................... 199
7.4.2 Smoothing Models ........................................................................................................... 203
7.4.2.4 Single Exponential Smoothing ...................................................................................... 203
7.4.2.5 Double Exponential Smoothing ..................................................................................... 204
7.4.2.6 Triple Exponential Smoothing (Holt-Winters model) ...................................................... 205
HOOFDSTUK 8: Univariate Box-Jenkins analyse ........................................................................ 211
8.2 Data .................................................................................................................................... 211
8.3 Theoretical Concepts .......................................................................................................... 212
8.3.0.1 Stationair Processes ..................................................................................................... 212

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