Fundamentals of Statistics

• Khan Academy: Statistics and Probability
• Coursera: Basic Statistics
• edX: Introduction to Probability and Data with R
• Udacity: Intro to Descriptive Statistics
• MIT OpenCourseWare: Introduction to Probability and Statistics

Probability Theory

• edX: Probability - The Science of Uncertainty and Data
• Coursera: Probability Theory: Foundation for Data Science
• Seeing Theory: A visual introduction to probability and statistics
• DataCamp: Foundations of Probability in Python
• MIT OpenCourseWare: Probabilistic Systems Analysis and Applied Probability

Inferential Statistics

• Coursera: Statistical Inference
• edX: Inference for Data Science
• DataCamp: Statistical Inference and Data Analysis
• MIT OpenCourseWare: Statistics for Applications
• Udacity: Intro to Inferential Statistics

Regression Analysis

• Coursera: Regression Models
• edX: The Analytics Edge
• DataCamp: Modeling with Data in the Tidyverse
• MIT OpenCourseWare: The Analytics Edge
• Udacity: Linear Regression

Bayesian Statistics

• Coursera: Bayesian Statistics: From Concept to Data Analysis
• edX: Bayesian Statistics: Techniques and Models
• DataCamp: Fundamentals of Bayesian Data Analysis in R
• MIT OpenCourseWare: Introduction to Probability and Statistics (Bayesian section)
• Coursera: Markov Chain Monte Carlo for Bayesian Inference

Multivariate Analysis

• Coursera: Applied Multivariate Statistical Analysis
• edX: Advanced Statistics for Data Science
• DataCamp: Multivariate Probability Distributions in Python
• MIT OpenCourseWare: Mathematical Statistics (Multivariate sections)
• Udacity: Multivariate Statistical Analysis

Machine Learning Statistics

• Coursera: Machine Learning by Andrew Ng
• edX: Machine Learning
• DataCamp: Machine Learning with caret in R
• MIT OpenCourseWare: Machine Learning
• fast.ai: Practical Deep Learning for Coders

Advanced Statistical Topics

• Coursera: Probabilistic Graphical Models
• edX: Statistical Learning
• DataCamp: Time Series Analysis in Python
• MIT OpenCourseWare: High-Dimensional Statistics
• Udacity: Time Series Forecasting

Statistical Programming

• Coursera: Data Science Specialization (R-focused)
• edX: Statistical Thinking in Python
• DataCamp: Statistical Thinking in Python
• The R Project: An Introduction to R
• Python.org: The Python Tutorial

Datasets and Data Repositories

• Kaggle Datasets
• U.S. Government's Open Data
• UCI Machine Learning Repository
• Gapminder: Data
• World Health Organization: Global Health Observatory data repository

Data Visualization

• Coursera: Information Visualization: Fundamentals
• edX: Data Visualization with Python
• DataCamp: Introduction to Data Visualization with ggplot2
• Plotly: Python Graphing Library
• D3.js - Data-Driven Documents

Free Statistics eBooks

• Think Stats: Exploratory Data Analysis in Python
• OpenIntro Statistics
• The Elements of Statistical Learning
• Forecasting: Principles and Practice

Statistical Research

• arXiv.org: Statistics - Machine Learning
• Journal of the American Statistical Association
• Annals of the Institute of Statistical Mathematics
• The Annals of Statistics