w203: Statistics for Data Science
Cover
I Probability Theory
1
Probability Spaces
1.1
Kolmogorov’s Axioms
1.2
Conditional Probability
2
Defining Random Variables
3
Summarizing Distributions
4
Conditional Expectation and the BLP
4.1
CEF Bivariate
4.2
(Optional) CEF Multivariate
4.3
Best Linear Predictor
II Learning from Data
5
Hypothesis Testing
6
Ordinary Least Squares
6.1
Solution of OLS
6.2
Errors and Residuals
6.3
Matrix Notation
6.4
An Example
6.5
Comparing the CEF, BLP, and Regression
6.6
Draw a Random Sample and Plot Them All!
7
Linear Conditional Expectation Function
7.1
Variance of Error
7.2
Variance of OLS Estimators
8
Large-Sample Regression
8.1
Consistency of OLS Estimators
8.2
Asymptotic Normality
8.3
Covariance Matrix Estimation
8.3.1
Heteroskedastic Variance
8.3.2
Homeskedastic Variance
References
Appendix
A
Matrix Algebra
B
Matrix Calculus
w203: Statistics for Data Science
Chapter 1
Probability Spaces