Statistics, probability, linear algebra, and mathematical foundations for data science

Statistics & Mathematics Mathematical foundations for data science, machine learning, and statistical analysis. Quick Start Core Concepts 1. Probability Distributions 2. Hypothesis Testing Framework 3. Linear Algebra Essentials 4. Regression Analysis Tools & Technologies Tool Purpose Version (2025) NumPy Numerical computing 1.26+ SciPy Scientific computing 1.12+ pandas Data manipulation 2.2+ statsmodels Statistical models 0.14+ scikit learn ML algorithms 1.4+ Troubleshooting Guide Issue Symptoms Root Cause Fix Low p value, small effect Significant but meaningless Large sample size Check effect size High variance Unstable estimates Small sample, outliers More data, robust methods Multicollinearity Inflated coefficients Correlated features VIF check, remove features Heteroscedasticity Invalid inference Non constant variance Weighted least squares Best Practices Resources [Khan Academy Statistics](https://www.khanacademy.org/math/statistics probability) [StatQuest with Josh Starmer](https://statquest.org/) "Introduction to Statistical Learning" (ISLR) Skill Certification Checklist: [ ] Can calculate descriptive statistics [ ] Can perform hypothesis tests (t test, chi square) [ ] Can implement A/B testing [ ] Can perform regression analysis [ ] Can use matrix operations for ML

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