Summary

Summary Statistics for Business

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Course
Statistics for Business (HSA10A)

Institution
Katholieke Universiteit Brussel (KUB)

This summary brings together all the information seen and discussed in statistics class, as well as my personal notes that helped me better understand the theory/exercises. I have included screenshots of calculations performed in Excel and highlighted or circled important numbers/figures in tables....

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Uploaded on August 22, 2023
Number of pages 113
Written in 2022/2023
Type Summary

statistics
business
business administration
bridging program
handelswetenschappen
schakelprogramma

Institution
Katholieke Universiteit Brussel (KUB)
Education
MBA
Course
Statistics for Business (HSA10A)

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Statisitcs
Contents
Language of data ..................................................................................................................................... 7
Stages in Quantitative Research.............................................................................................................. 7
Quantitative Research Question ............................................................................................................. 7
Quantitative vs. Qualitative research .................................................................................................. 7
Random experiment and variables ..................................................................................................... 7
Population ........................................................................................................................................... 8
Variables .............................................................................................................................................. 8
Classification of the variables .......................................................................................................... 9
Collect Data ........................................................................................................................................... 10
Population vs. Sample ....................................................................................................................... 10
Proper Sampling ................................................................................................................................ 10
Different Time Patterns ..................................................................................................................... 11
Data Matrix ........................................................................................................................................ 11
Descriptive Statistics ............................................................................................................................. 11
Qualitative Variables ......................................................................................................................... 11
Distribution of Outcomes: Frequency Analysis ............................................................................. 11
Summary Measures ....................................................................................................................... 12
Cumulative frequencies................................................................................................................. 12
Graphical Representation of Distribution of Outcomes ................................................................ 12
Quantitative Statistics ....................................................................................................................... 14
Distribution of outcomes and summary measures ....................................................................... 14
Distribution of Outcomes .............................................................................................................. 14
Discrete Variable (small number of outcomes)......................................................................... 14
Continuous variables or discrete with large number of outcomes ........................................... 15
Numerical Representation (Bins) .......................................................................................... 15
Graphical Representation...................................................................................................... 15
Summary Measures ....................................................................................................................... 17
Mean.......................................................................................................................................... 17
Variance and Standard Deviation .............................................................................................. 18
Skewness ................................................................................................................................... 19
Kurtosis ...................................................................................................................................... 19
Several measures for the center ............................................................................................... 19
Several measures for the spread ............................................................................................... 20
1

, Cumulative Distribution ................................................................................................................ 20
Interpretation ............................................................................................................................ 21
Interpolation.............................................................................................................................. 21
Quantile Function .......................................................................................................................... 22
Determining the kth- percentile with SPSS ................................................................................ 23
Quantiles to determine Summary Measures ............................................................................ 23
Distribution of Outcomes: BOXPLOT ..................................................................................... 24
Transformation of Data ................................................................................................................. 25
Logarithmic transformation ...................................................................................................... 25
Linear Transformation ............................................................................................................... 25
Summary Measures for Transformed Variables........................................................................ 25
Z-Score ....................................................................................................................................... 26
Binned Data ................................................................................................................................... 26
Cumulative Frequencies ............................................................................................................ 27
Interpolation for cumulative frequencies ............................................................................. 27
Percentiles ............................................................................................................................. 27
Summary Measures ................................................................................................................... 28
Relationships between variables....................................................................................................... 29
Distribution of combination of outcomes ..................................................................................... 29
Overview: Bivariate Descriptive Statistics ..................................................................................... 30
Relationships ................................................................................................................................. 31
Relationships between 2 Quantitative Variables .............................................................................. 31
Relationship between Quantitative and Qualitative Variables ......................................................... 33
Relationship between Quantitative Variables................................................................................... 33
Scatterplot ..................................................................................................................................... 33
Linear Association...................................................................................................................... 33
Covariance ................................................................................................................................. 34
Correlation................................................................................................................................. 34
Linear Combination of Variables ....................................................................................................... 35
Linear Transformation ................................................................................................................... 35
Linear Combination & Summary Measures .................................................................................. 36
Mean and variance for linear combinations ............................................................................. 36
Probability Theory ................................................................................................................................. 37
Definition ........................................................................................................................................... 37
Rules to determine probabilities ....................................................................................................... 37
Rule Laplace ................................................................................................................................... 37

2

, Counting Rules............................................................................................................................... 38
Axioms of Kolmogorov .................................................................................................................. 39
Conditional Probabilities ................................................................................................................... 40
General Multiplication Rule........................................................................................................... 40
Independence ................................................................................................................................ 41
Discrete Random Variables ............................................................................................................... 41
Random Variables.......................................................................................................................... 41
Probability Distribution for a Discrete Random Variable .............................................................. 42
Probability ..................................................................................................................................... 43
Cumulative Distribution ................................................................................................................ 43
Percentiles ..................................................................................................................................... 44
Summary Measures ....................................................................................................................... 44
Population Mean ....................................................................................................................... 44
Population Variance – Standard Deviation ............................................................................... 45
Binominal Distribution................................................................................................................... 45
Probability Distribution ............................................................................................................. 46
Expected Value (=Mean) and Variance ..................................................................................... 47
How the probability distribution looks like graphically............................................................. 47
Continuous Random Variable............................................................................................................ 47
Density ........................................................................................................................................... 47
Probability ..................................................................................................................................... 49
Cumulative Distribution ................................................................................................................ 49
Summary Measures ....................................................................................................................... 49
Continuous Distribution Models ................................................................................................... 51
Normal Distribution ................................................................................................................... 51
Parameter: ............................................................................................................................. 51
Probabilities:.......................................................................................................................... 51
Quantiles: .............................................................................................................................. 52
Normal Approximation: Normal Distribution for Binomial Distribution ................................... 52
Standard Normal Distribution ................................................................................................... 52
Linear Transformation & Combination for Discrete/continuous Random variables ........................ 54
Linear Transformation ................................................................................................................... 54
Linear critiions ............................................................................................................................... 54
Sums and Averages........................................................................................................................ 55
Expectation / Mean ................................................................................................................... 56
Variance ..................................................................................................................................... 56

3

, Distribution ................................................................................................................................ 57
Central Limit Theorem ................................................................................................................... 58
Conditions for applying the CLT ................................................................................................ 59
Foundation for Inference ...................................................................................................................... 60
Point Estimator .................................................................................................................................. 60
Confidence Interval ........................................................................................................................... 61
Ingredients..................................................................................................................................... 62
Determine the CI for mean µ ........................................................................................................ 62
Interpretation ................................................................................................................................ 63
Width of CI ..................................................................................................................................... 63
Assumptions .................................................................................................................................. 64
Basics of Hypothesis Tests ................................................................................................................. 64
All Steps ......................................................................................................................................... 65
Formulate hypotheses............................................................................................................... 65
Suitable Descriptive Statistics.................................................................................................... 66
P-value ....................................................................................................................................... 67
Conclusion ................................................................................................................................. 67
Assumptions .............................................................................................................................. 67
Two-Sided Test .......................................................................................................................... 67
Two-Sided Test with Confidence Intervals ............................................................................ 68
Right-Sided Test......................................................................................................................... 68
Critical Values and Power (Type 2 error)................................................................................... 68
Hypothesis Testing ................................................................................................................................ 70
H1Inference about means and correlations...................................................................................... 70
Hypothesis testing for one mean (sigma unknown)...................................................................... 70
Critical Value(s) ...................................................................................................................... 71
Confidence Interval ............................................................................................................... 72
SPSS ....................................................................................................................................... 72
Testing Normality .......................................................................................................................... 72
Kolmogorov-Smirnov test.......................................................................................................... 73
Shapiro-Wilk .............................................................................................................................. 75
Hypothesis testing to compare two means................................................................................... 75
Paired versus Unpaired ............................................................................................................. 75
Paired T-test → turns into t-test for one mean ........................................................................ 76
Confidence Interval ............................................................................................................... 77
Unpaired T-test → compares two means ................................................................................. 77

4

, (1) Test Statistics (known sigma): .......................................................................................... 78
(2) Test Statistics (unknown sigma):...................................................................................... 78
(3) Test statistic for (unknown) σ1= σ2:.................................................................................. 78
T-test to compare 2 means in SPSS ....................................................................................... 79
Confidence Intervals (unpaired means) ................................................................................ 79
Hypothesis Testing Compare More Than 2 Means – ANOVA ................................................... 80
Post-Hoc Test......................................................................................................................... 83
T-Test for Pearson Correlation .................................................................................................. 85
H2 Chi Square Test for goodness of Fit and Independence .............................................................. 87
Goodness Of Fit Test (Chi-Test) ..................................................................................................... 87
Independence (Chi Square Test) ................................................................................................... 90
5 Simple Linear Regression................................................................................................................ 93
SR_A Model Specification.............................................................................................................. 93
Assumptions .............................................................................................................................. 95
Nonlinear relationships ............................................................................................................. 96
Linear Model.......................................................................................................................... 98
Polynomial model: quadratic ................................................................................................ 98
Polynomial model: cubic ....................................................................................................... 98
Log transformation ................................................................................................................ 98
Log Linear Model ................................................................................................................... 99
Linear Log Model ................................................................................................................... 99
Log Log Model ....................................................................................................................... 99
Dummy Variable .................................................................................................................... 99
SR_B Inference about the regression parameters ...................................................................... 100
Fitted Model ............................................................................................................................ 100
Population vs. Estimated model .......................................................................................... 100
Least Squares Principles ...................................................................................................... 101
Residuals .............................................................................................................................. 101
Calculation LS (least squared) estimates ............................................................................. 102
Interpretation ...................................................................................................................... 102
Least Squares Prediction ..................................................................................................... 102
Estimate standard error of the model σ.............................................................................. 102
Properties of LSE...................................................................................................................... 103
Bi as a random variable ....................................................................................................... 103
Expected Value .................................................................................................................... 104
Variance ............................................................................................................................... 104

5

, Standard Error of the Parameters ....................................................................................... 104
Density ................................................................................................................................. 104
Gauss Markov theorem ....................................................................................................... 105
Interval estimation and hypothesis testing ............................................................................. 105
Confidence Interval for β1 ................................................................................................... 105
Hypothesis Testing .............................................................................................................. 106
SR_C Goodness of Fit ................................................................................................................... 108
Decomposition of variance and R-square ............................................................................... 108
Measuring Goodness of Fit.................................................................................................. 108
SR_D Checking Assumptions ....................................................................................................... 111
Assumption 1 ........................................................................................................................... 111
Assumption A2 ........................................................................................................................ 112
Assumption A3 ........................................................................................................................ 112
Assumption A4 ........................................................................................................................ 113
Assumption A5 ........................................................................................................................ 113

6

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