Contents
Essence of ’this’ Lecture Notes
1 Describing data
1.1 A taxonomy of data types
1.2 What is a "data set"?
1.3 Frequency
1.4 Representation of distributions
1.5 Measures of central tendency
1.6 Measures of dispersion
1.7 Measures of association for bivariate data
1.8 Issues of unit and scale
1.9 Chebyshev’s theorem (Chebyshev’s inequality)
1.10 Adding and multiplying terms over an index
2 Probability basics
2.1 Modeling a Random Experiment
2.2 Properties of a probability measure: Probability postulates
2.3 Probability versus possibility
2.4 Methods of assigning probability
2.5 Counting
2.6 Conditional probability
2.7 Bayes’ Theorem
2.8 Independence of events
2.9 Bivariate probabilities
2.10 Joint, marginal and conditional probabilities
2.11 Independence of Events
3 Random variables
3.1 Random Variables
3.2 Cumulative distribution function: CDF
3.3 Continuous and discrete random variables
3.4 Probability distribution functions
3.5 Expected Value
3.6 Variance and standard deviation
3.7 Random variables and distributions: Discrete probability laws
3.8 Random variables and distributions: Continuous probability laws
3.9 Random variables and distributions: Moments of distributions [Optional material]
3.10 Moment generating functions [Optional material]
3.11 Random vectors [Optional material]
4 Sampling distributions
4.1 Chebyshev’s theorem
4.2 Law of large numbers theorem
4.3 Central limit theorem
4.4 Distribution of sample means
5 Point estimators
5.1 Point estimation
5.2 Least squares technique: LS
5.3 Maximum likelihood technique: ML
5.4 Method of moments technique: MM
6 Confidence intervals
6.1 Confidence interval estimation: One population
6.2 Finite populations and correction
6.3 Sample size determination
6.4 Confidence interval estimation: Two populations
7 Hypothesis testing
7.1 Hypothesis testing: One population
7.2 Hypothesis testing: Two populations
7.3 p-value
7.4 Type I and Type II errors and the Power of a hypothesis test
8 Linear regression analysis
8.1 Overview of linear models
8.2 Transformations and functional forms
8.3 Our approach to teaching/learning
8.4 Building and estimating an Unconditional Model of Mean: A model which is a non-model
8.5 Building and estimating a Simple Linear Regression model
8.6 Building and estimating a Multiple Linear Regression model: An increase in dimensionality
8.7 Goodness of fit
8.8 Handling statistical uncertainty: calculation of variances and covariances associated with a Multiple Linear Regression model
8.9 Statistical inference
8.10 Essence of the Gauss-Markov assumptions
8.11 Model Specification
8.12 Regression analysis at work
8.13 Frisch-Waugh-Lovell theorem (FWL theorem)