Final Assignment 0HV130 - Exploratory Data Analysis Dashboard

Boxplot of penguin species body mass URL: https://allisonhorst.github.io/palmerpenguins/

An end-to-end analysis of continuous-time Markov chain (CTMC) convergence using uniformization. Covers generator matrix construction, Doeblin minorization, TV-distance mixing times across multiple initial distributions, expected reward convergence, and spectral gap analysis. Includes a structural comparison between dense and sparse transition matrices, with theoretical proofs for shared stationary distributions and Dobrushin's ergodicity theorem.

A regression analysis project modeling diamond prices using a 1,000-observation sample from a 54,000-record dataset. Covers simple and multiple linear regression, formal assumption diagnostics (linearity, constant variance, normality), log-transformation of the response variable, and model selection using adjusted R² and VIF. Includes confidence and prediction intervals for applied price forecasting.

A machine learning classification project predicting League of Legends match outcomes using interval snapshot data from 40,000 matches. Compares elastic net logistic regression, decision tree, random forest, and gradient boosted tree models via 5-fold cross-validation, achieving ROC AUC of 0.913. Includes cross-time analysis across 10–25 minute snapshots showing how prediction accuracy improves as the match progresses.