Business Statistics
26134
Business Statistics
Katie’s Notes
26134 Business Statistics
Contents Lecture 1 ................................................................................................................................................. 2 Types of Statistics: .............................................................................................................................. 3 Lecture 2 .................................................................................................. Error! Bookmark not defined. Measure of central tendency ............................................................... Error! Bookmark not defined. Measure of dispersion/spread ............................................................. Error! Bookmark not defined. Lecture 3 .................................................................................................. Error! Bookmark not defined. Types of bivariate relationship of quantitative variables ................ Error! Bookmark not defined. Lecture 4 .................................................................................................. Error! Bookmark not defined. Multiple Regression Model .................................................................. Error! Bookmark not defined. Building a Regression Model................................................................ Error! Bookmark not defined. R2 vs Adjusted R2 .................................................................................. Error! Bookmark not defined. Regression model evaluation: F test.................................................... Error! Bookmark not defined. Regression Model Significance: t test .................................................. Error! Bookmark not defined. Regression vs causality..................................................................... Error! Bookmark not defined. Lecture 5 .................................................................................................. Error! Bookmark not defined. Dummy Variables ................................................................................. Error! Bookmark not defined. Outliers................................................................................................. Error! Bookmark not defined. Multicollinearity ................................................................................... Error! Bookmark not defined. Nonlinearity ......................................................................................... Error! Bookmark not defined. Lecture 6 .................................................................................................. Error! Bookmark not defined. Terminology ......................................................................................... Error! Bookmark not defined. Mutually Exclusive Events .................................................................... Error! Bookmark not defined. “Special” Rule of Addition ................................................................ Error! Bookmark not defined. Probability of Non-mutually Exclusive Events ..................................... Error! Bookmark not defined. “General” Rule of Addition .............................................................. Error! Bookmark not defined. Contingency Tables .............................................................................. Error! Bookmark not defined. Conditional Probability ........................................................................ Error! Bookmark not defined. Independent Events ............................................................................. Error! Bookmark not defined. Joint probability of two independent events................................... Error! Bookmark not defined. Lecture 7 .................................................................................................. Error! Bookmark not defined. Random Variable.................................................................................. Error! Bookmark not defined. Probability Distribution ........................................................................ Error! Bookmark not defined. Continuous Probability Distribution ................................................ Error! Bookmark not defined. Probability Density Function ................................................................ Error! Bookmark not defined. Uniform distribution ........................................................................ Error! Bookmark not defined. 1|Page
26134 Business Statistics Normal Distribution ............................................................................. Error! Bookmark not defined. Probability Density Function of the Normal Distribution ................ Error! Bookmark not defined. Transforming to ‘Standard Normal Distribution’ ................................. Error! Bookmark not defined. Complement Rule ............................................................................ Error! Bookmark not defined. Symmetry Rule ................................................................................. Error! Bookmark not defined. Interval Rule ..................................................................................... Error! Bookmark not defined. Lecture 8 .................................................................................................. Error! Bookmark not defined. Relevance of Sampling Distributions ................................................... Error! Bookmark not defined. Central Limit Theorem ......................................................................... Error! Bookmark not defined. Sampling distribution of the Sample Mean ......................................... Error! Bookmark not defined. Sampling distribution of the sample proportion ................................. Error! Bookmark not defined. Lecture 9 .................................................................................................. Error! Bookmark not defined. Motivation-Point Estimator ................................................................. Error! Bookmark not defined. Motivation-Interval Estimator ............................................................. Error! Bookmark not defined. Interval Estimates: Interpretation ................................................... Error! Bookmark not defined. Constructing a Confidence Interval ..................................................... Error! Bookmark not defined. Calculating CI if σ is unknown .............................................................. Error! Bookmark not defined. t-distribution characteristics ............................................................ Error! Bookmark not defined. Calculating CI using t-statistic .......................................................... Error! Bookmark not defined. Determining the appropriate sample size ........................................... Error! Bookmark not defined. Confidence Interval of Population Proportion..................................... Error! Bookmark not defined. Minimum sample size ...................................................................... Error! Bookmark not defined. Lecture 10 ................................................................................................ Error! Bookmark not defined. Hypothesis testing................................................................................ Error! Bookmark not defined. Type I and Type II errors ...................................................................... Error! Bookmark not defined. Summary-Steps in Hypothesis Testing ................................................. Error! Bookmark not defined. Hypothesis testing if sigma (pop. standard dev. is unknown) ............. Error! Bookmark not defined.
2|Page
26134 Business Statistics
Lecture 1 Self-study topics won’t be in quizzes and finals, but can be in the assignment. Threshold Concept 1: identifying relevant data, measurement properties of data For QUIZ 1
Types of Statistics:
Descriptive statistics: collecting (e.g. survey), summarising and describing o Process: collecting, summarising and then characterising (focus is on). and Inferential statistics: inferring data; drawing conclusions and/or making decisions concerning a population based only on sample data o Process: estimation hypothesis testing (TH2)
A population is a collection of all possible individuals, objects, or measurements of interest. A sample is a portion, part, or subset of the population of interest.
(basis of TH1. v imp) Nominal: data that is classified into non-overlapping categories and cannot be arranged in any particular order/sorted. (e.g. eye colour, gender, TV brands) Ordinal level: data that is classified into distinct non-overlapping categories in which ranking is implied. i.e. data can be arranged into some sort of order/sorted. (e.g. test performance is graded as HD, D, C, P or F.) Interval level: an ordered scale in which the difference between measurements is a meaningful quantity (e.g. test scores HD is 85+, D is 65-75, etc ) but the measurements do not have a true zero point. (e.g. shoe size; size 0 does not mean there is no shoe) Ratio level: the interval level with an inherent zero starting point. differences and ratios are meaningful for this level of measurement. ‘zero’ is significant. (e.g. price, distance travelled to destination, time taken to reach a destination)
3|Page
Business Statistics
Katie’s Notes
26134 Business Statistics
Contents Lecture 1 ................................................................................................................................................. 2 Types of Statistics: .............................................................................................................................. 3 Lecture 2 .................................................................................................. Error! Bookmark not defined. Measure of central tendency ............................................................... Error! Bookmark not defined. Measure of dispersion/spread ............................................................. Error! Bookmark not defined. Lecture 3 .................................................................................................. Error! Bookmark not defined. Types of bivariate relationship of quantitative variables ................ Error! Bookmark not defined. Lecture 4 .................................................................................................. Error! Bookmark not defined. Multiple Regression Model .................................................................. Error! Bookmark not defined. Building a Regression Model................................................................ Error! Bookmark not defined. R2 vs Adjusted R2 .................................................................................. Error! Bookmark not defined. Regression model evaluation: F test.................................................... Error! Bookmark not defined. Regression Model Significance: t test .................................................. Error! Bookmark not defined. Regression vs causality..................................................................... Error! Bookmark not defined. Lecture 5 .................................................................................................. Error! Bookmark not defined. Dummy Variables ................................................................................. Error! Bookmark not defined. Outliers................................................................................................. Error! Bookmark not defined. Multicollinearity ................................................................................... Error! Bookmark not defined. Nonlinearity ......................................................................................... Error! Bookmark not defined. Lecture 6 .................................................................................................. Error! Bookmark not defined. Terminology ......................................................................................... Error! Bookmark not defined. Mutually Exclusive Events .................................................................... Error! Bookmark not defined. “Special” Rule of Addition ................................................................ Error! Bookmark not defined. Probability of Non-mutually Exclusive Events ..................................... Error! Bookmark not defined. “General” Rule of Addition .............................................................. Error! Bookmark not defined. Contingency Tables .............................................................................. Error! Bookmark not defined. Conditional Probability ........................................................................ Error! Bookmark not defined. Independent Events ............................................................................. Error! Bookmark not defined. Joint probability of two independent events................................... Error! Bookmark not defined. Lecture 7 .................................................................................................. Error! Bookmark not defined. Random Variable.................................................................................. Error! Bookmark not defined. Probability Distribution ........................................................................ Error! Bookmark not defined. Continuous Probability Distribution ................................................ Error! Bookmark not defined. Probability Density Function ................................................................ Error! Bookmark not defined. Uniform distribution ........................................................................ Error! Bookmark not defined. 1|Page
26134 Business Statistics Normal Distribution ............................................................................. Error! Bookmark not defined. Probability Density Function of the Normal Distribution ................ Error! Bookmark not defined. Transforming to ‘Standard Normal Distribution’ ................................. Error! Bookmark not defined. Complement Rule ............................................................................ Error! Bookmark not defined. Symmetry Rule ................................................................................. Error! Bookmark not defined. Interval Rule ..................................................................................... Error! Bookmark not defined. Lecture 8 .................................................................................................. Error! Bookmark not defined. Relevance of Sampling Distributions ................................................... Error! Bookmark not defined. Central Limit Theorem ......................................................................... Error! Bookmark not defined. Sampling distribution of the Sample Mean ......................................... Error! Bookmark not defined. Sampling distribution of the sample proportion ................................. Error! Bookmark not defined. Lecture 9 .................................................................................................. Error! Bookmark not defined. Motivation-Point Estimator ................................................................. Error! Bookmark not defined. Motivation-Interval Estimator ............................................................. Error! Bookmark not defined. Interval Estimates: Interpretation ................................................... Error! Bookmark not defined. Constructing a Confidence Interval ..................................................... Error! Bookmark not defined. Calculating CI if σ is unknown .............................................................. Error! Bookmark not defined. t-distribution characteristics ............................................................ Error! Bookmark not defined. Calculating CI using t-statistic .......................................................... Error! Bookmark not defined. Determining the appropriate sample size ........................................... Error! Bookmark not defined. Confidence Interval of Population Proportion..................................... Error! Bookmark not defined. Minimum sample size ...................................................................... Error! Bookmark not defined. Lecture 10 ................................................................................................ Error! Bookmark not defined. Hypothesis testing................................................................................ Error! Bookmark not defined. Type I and Type II errors ...................................................................... Error! Bookmark not defined. Summary-Steps in Hypothesis Testing ................................................. Error! Bookmark not defined. Hypothesis testing if sigma (pop. standard dev. is unknown) ............. Error! Bookmark not defined.
2|Page
26134 Business Statistics
Lecture 1 Self-study topics won’t be in quizzes and finals, but can be in the assignment. Threshold Concept 1: identifying relevant data, measurement properties of data For QUIZ 1
Types of Statistics:
Descriptive statistics: collecting (e.g. survey), summarising and describing o Process: collecting, summarising and then characterising (focus is on). and Inferential statistics: inferring data; drawing conclusions and/or making decisions concerning a population based only on sample data o Process: estimation hypothesis testing (TH2)
A population is a collection of all possible individuals, objects, or measurements of interest. A sample is a portion, part, or subset of the population of interest.
(basis of TH1. v imp) Nominal: data that is classified into non-overlapping categories and cannot be arranged in any particular order/sorted. (e.g. eye colour, gender, TV brands) Ordinal level: data that is classified into distinct non-overlapping categories in which ranking is implied. i.e. data can be arranged into some sort of order/sorted. (e.g. test performance is graded as HD, D, C, P or F.) Interval level: an ordered scale in which the difference between measurements is a meaningful quantity (e.g. test scores HD is 85+, D is 65-75, etc ) but the measurements do not have a true zero point. (e.g. shoe size; size 0 does not mean there is no shoe) Ratio level: the interval level with an inherent zero starting point. differences and ratios are meaningful for this level of measurement. ‘zero’ is significant. (e.g. price, distance travelled to destination, time taken to reach a destination)
3|Page
