Statistics & Probability

From raw data to actionable insights. We explain the "black box" formulas of statistics.

Descriptive Statistics

• Variance & Standard Deviation - Measuring spread.
• Covariance - Measuring how two variables change together.
• Moments - The mathematical shape of data.

Distributions

• Bernoulli Distribution - The fundamental binary distribution.
• Gaussian (Normal) Distribution - The bell curve derived.
• Student's t-Distribution - Dealing with small sample sizes.
• Central Limit Theorem - Why everything becomes normal when averaged.
• Student's t-Test - How to test hypotheses.
• F-Test - Comparing variances.
• Chi-Squared Test - Testing categorical data.

Regression (SLR)

Simple Linear Regression explained from the ground up.

• OLS Estimators - Deriving \(\beta_0\) and \(\beta_1\).
• Slope Properties - Expectation and Variance of the slope.
• Intercept Properties - Expectation and Variance of the intercept.
• Mean Response - Predicting the average \(y\).
• R-Squared - How well does the model fit?
• Cook's Distance - Detecting influential observations.

Inference & Correlation

• Pearson's Correlation - Linear relationships.
• Spearman's Correlation - Rank-based relationships.
• Confidence Interval - Determining uncertainty.
• Prediction Interval - Predicting the next value.
• Method of Moments - A technique for estimating parameters.
• Likelihood-Based Statistics - MLE and likelihood theory.
• Sample Mean Estimator - Properties, derivation, and standard error.
• Regression Trees, Bagging, and Boosting - Ensemble methods for prediction.